Questions · Page 3 of 11

MCQ

MCQ 1011 Mark
A soap bubble in vacuum has a radius of $3 \mathrm{~cm}$ and another soap bubble in vacuum has a radius of $4 \mathrm{~cm}$. If the two bubbles coalesce under isothermal condition, then the radius of the new bubble is
  • A
    $2.3 \mathrm{~cm}$
  • B
    $4.5 \mathrm{~cm}$
  • $5 \mathrm{~cm}$
  • D
    $7 \mathrm{~cm}$
Answer
Correct option: C.
$5 \mathrm{~cm}$
(c) $r=\sqrt{r_1^2+r_2^2}=\sqrt{9+16}=5 \mathrm{~cm}$
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MCQ 1021 Mark
A car of mass ' $m$ ' is driven with acceleration ' $a$ ' along a straight level road against a constant external resistive force ' $R$. When the velocity of the car is ' $V$, the rate at which the engine of the car is doing work will be
  • A
    $R V$
  • B
    $\mathrm{maV}$
  • $(R+m a) V$
  • D
    $(m a-R) V$
Answer
Correct option: C.
$(R+m a) V$
Force required to move with constant velocity
$\therefore$ Power $=F V$ Forceisrequired to oppose the resistive force $R$ and also to accelerate the body of mass with acceleration$a$).
$\therefore$ Power $=(R+m a) V$
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MCQ 1031 Mark
A particle of mass $m$ moving with velocity $v$ strikes a stationary particle of mass $2 \mathrm{~m}$ and sticks to it. The speed of the system will be
  • A
    $v / 2$
  • B
    $2 \mathrm{v}$
  • $v / 3$
  • D
    $3 v$
Answer
Correct option: C.
$v / 3$
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MCQ 1041 Mark
At which of the following temperatures, the value of surface tension of water is minimum
  • A
    $4 \mathrm{C}$
  • B
    $25 . \mathrm{C}$
  • C
    $50 \cdot \mathrm{C}$
  • $75 . \mathrm{C}$
Answer
Correct option: D.
$75 . \mathrm{C}$
$75 . \mathrm{C}$
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MCQ 1051 Mark
A frictionless track $A B C D E$ ends in a circular loop of radius $R$. A body slides down the track from point $A$ which is at $a$ height $h=5$ $\mathrm{cm}$. Maximum value of $R$ for the body to successfully complete the loop isImage
  • A
    $5 \mathrm{~cm}$
  • B
    $\frac{15}{4} \mathrm{~cm}$
  • C
    $\frac{10}{3} \mathrm{~cm}$
  • $2 \mathrm{~cm}$
Answer
Correct option: D.
$2 \mathrm{~cm}$
From the conservation of energy,
$mgh =\frac{1}{2} mv ^2 $
$v =\sqrt{2 gh }$
The condition for completing the loop is given as,
$\sqrt{2 g h}=\sqrt{5 g R} $
$R=\frac{2 \times 5}{5} $
$=2\ cm$
Thus, the maximum value of $R$ for the body to successfully complete the loop is $2\ cm .$
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MCQ 1061 Mark
Two soap bubbles have different radii but their surface tension is the same. Mark the correct statement
  • Internal pressure of the smaller bubble is higher than the internal pressure of the larger bubble
  • B
    Pressure of the larger bubble is higher than the smaller bubble
  • C
    Both bubbles have the same internal pressure
  • D
    None of the above
Answer
Correct option: A.
Internal pressure of the smaller bubble is higher than the internal pressure of the larger bubble
(a)$\Delta P=\frac{4 T}{R} \therefore \Delta P \propto \frac{1}{R} \quad(T=\text { constant })$Hence, the internal pressure of smaller bubble is larger than that of larger bubble.
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MCQ 1071 Mark
A particle of mass $\mathrm{m}$ moving with horizontal speed $6 \mathrm{~m} / \mathrm{sec}$ as shown in figure. If $m \ll M$ then for one dimensional elastic collision, the speed of lighter particle after collision will be

Image

  • $2 \mathrm{~m} / \mathrm{sec}$ in original direction
  • B
    $2 \mathrm{~m} / \mathrm{sec}$ opposite to the original direction
  • C
    $4 \mathrm{~m} / \mathrm{sec}$ opposite to the original direction
  • D
    $4 \mathrm{~m} / \mathrm{sec}$ in original direction
Answer
Correct option: A.
$2 \mathrm{~m} / \mathrm{sec}$ in original direction
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MCQ 1081 Mark
If a long spring is stretched by $0.02 \mathrm{~m}$, its potential energy is $U$. If the spring is stretched by $0.1 \mathrm{~m}$, then its potential energy will be
  • A
    $\frac{U}{5}$
  • B
    $U$
  • C
    $5 \ U$
  • $25\  \mathrm{U}$
Answer
Correct option: D.
$25\  \mathrm{U}$
(d) $U \propto x^2 \Rightarrow \frac{U_2}{U_1}=\left(\frac{x_2}{x_1}\right)^2=\left(\frac{0.1}{0.02}\right)^2=25 \therefore U_2=25 \ U$
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MCQ 1091 Mark
Two soap bubbles of radii $r_1$ and $r_2$ equal to $4 \mathrm{~cm}$ and $5 \mathrm{~cm}$ are touching each other over a common surface $S_1 S_2$ (shown in figure). Its radius will be
Image
  • A
    $4 \mathrm{~cm}$
  • $20 \mathrm{~cm}$
  • C
    $5 \mathrm{~cm}$
  • D
    $4.5 \mathrm{~cm}$
Answer
Correct option: B.
$20 \mathrm{~cm}$
(b) $\quad r=\frac{r_1 r_2}{r_1-r_2}=\frac{5 \times 4}{5-4}=20 \mathrm{~cm}$
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MCQ 1101 Mark
Two capillary tubes of same diameter are put vertically one each in two liquids whose relative densities are 0.8 and 0.6 and surface tensions are 60 and $50 \mathrm{dyne} / \mathrm{cm}$ respectively Ratio of heights of liquids in the two tubes $\frac{h_1}{h_2}$ is
  • A
    $\frac{10}{9}$
  • B
    $\frac{3}{10}$
  • C
    $\frac{10}{3}$
  • $\frac{9}{10}$
Answer
Correct option: D.
$\frac{9}{10}$
(d) Ascent formula $h=\frac{2 T \cos \theta}{r d g}$
$ \Rightarrow \frac{h_1}{h_2}=\frac{T_1}{T_2} \times \frac{d_2}{d_1} \quad(r, \theta \text { and } g \text { are constants })$
$ =\frac{60}{50} \times \frac{0.6}{0.8}=\frac{9}{10}$
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MCQ 1111 Mark
A ball of mass $m$ moving with velocity $V$, makes a head on elastic collision with a ball of the same mass moving with velocity $2 \mathrm{~V}$ towards it. Taking direction of $V$ as positive velocities of the two balls after collision are
  • A
    $-V$ and $2 V$
  • B
    $2 V$ and $-V$
  • C
    $V$ and $-2 V$
  • $-2 V$ and $V$
Answer
Correct option: D.
$-2 V$ and $V$
(d) Due to elastic collision of bodies having equal mass, their velocities get interchanged.
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MCQ 1121 Mark
The radii of two soap bubbles are $r$ and $r$. In isothermal conditions, two meet together in vaccum. Then the radius of the resultant bubble is given by
  • A
    $R=\left(r_1+r_2\right) / 2$
  • B
    $R=r_1\left(r_1 r_2+r_2\right)$
  • $R^2=r_1^2+r_2^2$
  • D
    $R=r_1+r_2$
Answer
Correct option: C.
$R^2=r_1^2+r_2^2$
(c)
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MCQ 1131 Mark
Water rises to a height $h$ in a capillary at the surface of earth. On the surface of the moon the height of water column in the same capillary will be
  • $6 h$
  • B
    $\frac{1}{6} h$
  • C
    $h$
  • D
    Zero
Answer
Correct option: A.
$6 h$
(a) $h=\frac{2 T \cos \theta}{r d g} \therefore h \propto \frac{1}{g}$As $g_m=\frac{g_e}{6} \therefore h_m=6 h_e$
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MCQ 1141 Mark
A particle of mass $m$ moving with a velocity $\vec{V}$ makes a head on elastic collision with another particle of same mass initially at rest. The velocity of the first particle after the collision will be
  • A
    $\vec{V}$
  • B
    $-\vec{V}$
  • C
    $-2 \vec{V}$
  • Zero
Answer
Correct option: D.
Zero
(d) In perfectly elastic head on collision of equal masses velocities gets interchanged
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MCQ 1151 Mark
If a lighter body $($mass $M_1$ and velocity $V_1 )$ and a heavier body $($mass $M_2$ and velocity $V_2 )$ have the same kinetic energy, then
  • A
    $M_2 V_2$
  • B
    $M_2 V_2=M_1 V_1$
  • C
    $M_2 V_1=M_1 V_2$
  • $M_2 V_2>M_1 V_1$
Answer
Correct option: D.
$M_2 V_2>M_1 V_1$
$M_2 V_2>M_1 V_1$
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MCQ 1161 Mark
The amount of work done in blowing a soap bubble such that its diameter increases from $d$ to $D$ is ( $T$ = surface tension of the solution)
  • A
    $4 \pi\left(D^2-d^2\right) T$
  • B
    $8 \pi\left(D^2-d^2\right) T$
  • C
    $\pi\left(D^2-d^2\right) T$
  • $2 \pi\left(D^2-d^2\right) T$
Answer
Correct option: D.
$2 \pi\left(D^2-d^2\right) T$
$ W=T \times 8 \pi\left(r_2^2-r_1^2\right)=T \times 8 \pi\left(\frac{D^2}{4}-\frac{d^2}{4}\right)$
$ =2 \pi\left(D^2-d^2\right) T$
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MCQ 1171 Mark
When two soap bubbles of radius $r_1$ and $r_2\left(r_2>r_1\right)$ coalesce, the radius of curvature of common surface is
  • A
    $r_2-r_1$
  • B
    $\frac{r_2-r_1}{r_1 r_2}$
  • $\frac{r_1 r_2}{r_2-r_1}$
  • D
    $r_2+r_1$
Answer
Correct option: C.
$\frac{r_1 r_2}{r_2-r_1}$
(c)
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MCQ 1181 Mark
A force $\boldsymbol{F}=(5 \hat{\boldsymbol{i}}+3 \hat{\boldsymbol{j}})$ newton is applied over a particle which displaces it from its origin to the point $\boldsymbol{r}=(2 \hat{i}-1 \hat{\boldsymbol{j}})$ metres. The work done on the particle is
  • A
    -7 joules
  • B
    +13 joules
  • +7 joules
  • D
    +11 joules
Answer
Correct option: C.
+7 joules
(c) $W=\vec{F} \cdot \vec{s}=(5 \hat{i}+3 \hat{j}) \cdot(2\hat{i}\hat{j})=10-3=7\mathrm{~J}$
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MCQ 1191 Mark
The work done in blowing a soap bubble of $10 \mathrm{~cm}$ radius is (Surface tension of the soap solution is $\frac{3}{100} \mathrm{~N} / \mathrm{m}$ )
  • $75.36 \times 10^{-4}$ joule
  • B
    $37.68 \times 10^{-4}$ joule
  • C
    $150.72 \times 10^{-4}$ joule
  • D
    75.36joule
Answer
Correct option: A.
$75.36 \times 10^{-4}$ joule
(a) $W=8 \pi R^2 T=8 \times 3.14 \times\left(10 \times 10^{-2}\right) \times \frac{3}{100}$
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MCQ 1201 Mark
A body of mass $m$ having an initial velocity $v$, makes head on collision with a stationary body of mass $M$. After the collision, the body of mass $m$ comes to rest and only the body having mass $M$ moves. This will happen only when
  • A
    $m \gg M$
  • B
    $m<<\ M$
  • $m=M$
  • D
    $m=\frac{1}{2} M$
Answer
Correct option: C.
$m=M$
(c) Velocity exchange takes place when the masses of bodies are equal
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MCQ 1211 Mark
If temperature increases, the surface tension of a liquid
  • A
    Increases
  • Decreases
  • C
    Remains the same
  • D
    Increases then decreases
Answer
Correct option: B.
Decreases
(b)
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MCQ 1221 Mark
If the kinetic energy of a body increases by $0.1 \%$, the percent increase of its momentum will be
  • $0.05 \%$
  • B
    $0.1 \%$
  • C
    $1.0 \%$
  • D
    $10 \%$
Answer
Correct option: A.
$0.05 \%$
(a) $P=\sqrt{2 m E} \therefore P \propto \sqrt{E}$Percentage increase in $P=\frac{1}{2}$ (percentage increase in $E$ )$=\frac{1}{2}(0.1 \%)=0.05 \%$
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MCQ 1231 Mark
The potential energy of a molecule on the surface of liquid compared to one inside the liquid is
  • A
    Zero
  • B
    Smaller
  • C
    The same
  • Greater
Answer
Correct option: D.
Greater
(d)
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MCQ 1241 Mark
A body of mass $m \mathrm{~kg}$ is lifted by a man to a height of one metre in $30 \mathrm{sec}$. Another man lifts the same mass to the same height in 60 sec. The work done by them are in the ratio
  • A
    $1: 2$
  • $1: 1$
  • C
    $2: 1$
  • D
    $4: 1$
Answer
Correct option: B.
$1: 1$
(b) Work done does not depend on time.
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MCQ 1251 Mark
Force necessary to pull a circular plate of $5 \mathrm{~cm}$ radius from water surface for which surface tension is 75 dynes $/ \mathrm{cm}$, is
  • A
    30dyne
  • B
    60 dynes
  • C
    750 dynes
  • $750 \pi$ dynes
Answer
Correct option: D.
$750 \pi$ dynes
(d) The total length of the circular plate on which the force will act $=2 \pi R$Force to pull $=2 \pi R T=2 \times \pi \times 5 \times 75=750 \pi$ dynes
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MCQ 1261 Mark
Surface tension of a soap solution is $1.9 \times 10^{-2} \mathrm{~N} / \mathrm{m}$. Work done in blowing a bubble of $2.0 \mathrm{~cm}$ diameter will be
  • A
    $7.6 \times 10^{-6} \pi$ joule
  • $15.2 \times 10^{-6} \pi$ joule
  • C
    $1.9 \times 10^{-6} \pi$ joule
  • D
    $1 \times 10^{-4}$ joule
Answer
Correct option: B.
$15.2 \times 10^{-6} \pi$ joule
(b) $W=8 \pi R^2 T=8 \pi \times\left(1 \times 10^{-2}\right)^2 \times 1.9 \times 10^{-2}=15.2 \times 10^{-6} \pi J$
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MCQ 1271 Mark
Pressure inside two soap bubbles are $1.01$ and $1.02$ atmospheres. Ratio between their volumes is
  • A
    $102: 101$
  • B
    $(102):(101)$
  • $8: 1$
  • D
    $2: 1$
Answer
Correct option: C.
$8: 1$
Outside pressure $=1 \mathrm{~atm}$
Pressure inside first bubble $=1.01 \mathrm{~atm}$
Pressure inside second bubble $=1.02 \mathrm{~atm}$
Excess pressure $\Delta P_1=1.01-1=0.01 \mathrm{~atm}$
Excess pressure $\Delta P_2=1.02-1=0.02 \mathrm{~atm}$
$\Delta P \propto \frac{1}{r} \Rightarrow r \propto \frac{1}{\Delta P}\Rightarrow \frac{r_1}{r_2}=\frac{\Delta P_2}{\Delta P_1}=\frac{0.02}{0.01}=\frac{2}{1}$
Since $V=\frac{4}{3} \pi r^3 \quad \therefore \frac{V_1}{V_2}=\left(\frac{r_1}{r_2}\right)^3=\left(\frac{2}{1}\right)^3=\frac{8}{1}$
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MCQ 1281 Mark
Water rises upto $10 \mathrm{~cm}$ height in a long capillary tube. If this tube is immersed in water so that the height above the water surface is only $8 \mathrm{~cm}$, then
  • A
    Water flows out continuously from the upper end
  • Water rises upto upper end and forms a spherical surface
  • C
    Water only rises upto $6 \mathrm{~cm}$ height
  • D
    Water does not rise at all
Answer
Correct option: B.
Water rises upto upper end and forms a spherical surface
(b)
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MCQ 1291 Mark
A square frame of side $\mathrm{L}$ is dipped in a liquid. On taking out, a membrane is formed. If the surface tension of the liquid is $T$, the force acting on the frame will be
  • A
    $2 T L$
  • B
    $4 T L$
  • $8 T L$
  • D
    $10 \mathrm{TL}$
Answer
Correct option: C.
$8 T L$
(c) Force on each side $=2 T L$ (due to two surfaces)$\therefore$ Force on the frame $=4(2 T L)=8 T L$
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MCQ 1301 Mark
A long cylindrical glass vessel has a small hole of radius ' $r$ ' at its bottom. The depth to which the vessel can be lowered vertically in the deep water bath $($surface tension $T )$ without any water entering inside is
  • A
    $477 \rho r g$
  • B
    $377 \rho r g$
  • $27 / \rho r g$
  • D
    $\mathrm{T} / \rho r g$
Answer
Correct option: C.
$27 / \rho r g$
$h d g=\frac{2 T}{r} \Rightarrow h=\frac{2 T}{r d g}$
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MCQ 1311 Mark
The excess of pressure inside a soap bubble than that of the outer pressure is
  • A
    $\frac{2 T}{r}$
  • $\frac{4 T}{r}$
  • C
    $\frac{T}{2 r}$
  • D
    $\frac{T}{r}$
Answer
Correct option: B.
$\frac{4 T}{r}$
(b)
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MCQ 1321 Mark
In the glass capillary tube, the shape of the surface of the liquid depends upon
  • A
    Only on the cohesive force of liquid molecules
  • B
    Only on the adhesive force between the molecules of glass and liquid
  • Only on relative cohesive and adhesive force between the atoms
  • D
    Neither on cohesive nor on adhesive force
Answer
Correct option: C.
Only on relative cohesive and adhesive force between the atoms
(c)
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MCQ 1331 Mark
The surface tension of a soap solution is $2 \times 10^{-2} \mathrm{~N} / \mathrm{m}$. To blow a bubble of radius $1 \mathrm{~cm}$, the work done is
  • A
    $4 \pi \times 10^{-6} J$
  • B
    $8 \pi \times 10^{-6} \mathrm{~J}$
  • C
    $12 \pi \times 10^{-6} J$
  • $16 \pi \times 10^{-6} \mathrm{~J}$
Answer
Correct option: D.
$16 \pi \times 10^{-6} \mathrm{~J}$
(d) $W=8 \pi R^2 T=8 \times \pi \times\left(10^{-2}\right)^2 \times 2 \times 10^{-2}=16 \pi \times 10^{-6} J$
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MCQ 1341 Mark
The excess pressure due to surface tension in a spherical liquid drop of radius $r$ is directly proportional to
  • A
    $r$
  • B
    $r^2$
  • $r^{-1}$
  • D
    $r^{-2}$
Answer
Correct option: C.
$r^{-1}$
(c)
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MCQ 1351 Mark
The angle of contact between glass and mercury is
  • A
    $0^{\circ}$
  • B
    $30$
  • C
    $90$
  • $135$
Answer
Correct option: D.
$135$
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MCQ 1361 Mark
The radius of a soap bubble is increased from $\frac{1}{\sqrt{\pi}} \mathrm{cm}$ to $\frac{2}{\sqrt{\pi}} \mathrm{cm}$. If the surface tension of water is $30$ dynes per $\mathrm{cm}$, then the work done will be
  • A
    $180$ ergs
  • B
    $360$ ergs
  • $720$ ergs
  • D
    $960$ ergs
Answer
Correct option: C.
$720$ ergs
$ W=8 \pi T\left(r_2^2-r_1^2\right)=8 \pi T\left[\left(\frac{2}{\sqrt{\pi}}\right)^2-\left(\frac{1}{\sqrt{\pi}}\right)^2\right]  \therefore W=8 \times \pi \times 30 \times \frac{3}{\pi}=720\  \mathrm{erg}$
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MCQ 1371 Mark
Two bodies of masses $m_1$ and $m_2$ have equal kinetic energies. If $p_1$ and $p_2$ are their respective momentum, then ratio $p_1: p_2$ is equal to
  • A
    $m_1: m_2$
  • B
    $m_2: m_1$
  • $\sqrt{m_1}: \sqrt{m_2}$
  • D
    $m_1^2: m_2^2$
Answer
Correct option: C.
$\sqrt{m_1}: \sqrt{m_2}$
(c) $\quad P=\sqrt{2 m E} \quad \therefore P\propto\sqrt{m} (if)(E)=$ const
$(\therefore\frac{P_1}{P_2}=\sqrt{\frac{m_1}{m_2}})$
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MCQ 1381 Mark
A light and a heavy body have equal momenta. Which one has greater $K.E$
  • The light body
  • B
    The heavy body
  • C
    The $K.E$. are equal
  • D
    Data is incomplete
Answer
Correct option: A.
The light body
The light body
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MCQ 1391 Mark
Two capillary tubes $P$ and $Q$ are dipped in water. The height of water level in capillary $P$ is $2 / 3$ to the height in $Q$ capillary. The ratio of their diameters is
  • $2: 3$
  • B
    $3: 2$
  • C
    $3: 4$
  • D
    $4: 3$
Answer
Correct option: A.
$2: 3$
(b) $r \propto \frac{1}{h} \Rightarrow \frac{r_P}{r_Q}=\frac{h_Q}{h_P}=\frac{h}{\frac{2}{3} h}=\frac{2}{3}$
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MCQ 1401 Mark
A mercury drop does not spread on a glass plate because the angle of contact between glass and mercury is
  • A
    Acute
  • Obtuse
  • C
    Zero
  • D
    $90^{\circ}$
Answer
Correct option: B.
Obtuse
(b)
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MCQ 1411 Mark
The surface tension of a liquid at its boiling point
  • Becomes zero
  • B
    Becomes infinity
  • C
    is equal to the value at room temperature
  • D
    is half to the value at the room temperature
Answer
Correct option: A.
Becomes zero
(a)
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MCQ 1421 Mark
Work done in splitting a drop of water of $1 \mathrm{~mm}$ radius into 10 droplets is (Surface tension of water $=72 \times 10^{-3} \mathrm{~J} / \mathrm{m}^2$ )
  • A
    $9.58 \times 10^{-5} J$
  • $8.95 \times 10^{-5} J$
  • C
    $5.89 \times 10^{-5} J$
  • D
    $5.98 \times 10^{-6} J$
Answer
Correct option: B.
$8.95 \times 10^{-5} J$
(b) Work done in splitting a water drop of radius $R$ into $n$ drops of equal size $=4 \pi R^2 T\left(n^{1 / 3}-1\right)$$\begin{aligned}& =4 \pi \times\left(10^{-3}\right)^2 \times 72 \times 10^{-3} \times\left(10^{6 / 3}-1\right) \\& =4 \pi \times 10^{-6} \times 72 \times 10^{-3} \times 99=8.95 \times 10^{-5} \mathrm{~J}\end{aligned}$
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MCQ 1431 Mark
A pin or a needle floats on the surface of water, the reason for this is
  • Surface tension
  • B
    Less weight
  • C
    Upthrust of liquid
  • D
    None of the above
Answer
Correct option: A.
Surface tension
(a)
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MCQ 1441 Mark
The meniscus of mercury in the capillary tube is
  • Convex
  • B
    Concave
  • C
    Plane
  • D
    Uncertain
Answer
Correct option: A.
Convex
(a)
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MCQ 1451 Mark
The kinetic energy of a body of mass $3 \mathrm{~kg}$ and momentum $2 \mathrm{Ns}$ is
  • A
    $11\mathrm{~J}$
  • $\frac{2}{3} \mathrm{~J}$
  • C
    $\frac{3}{2}\ \mathrm{~J}$
  • D
    $4 \mathrm{~J}$
Answer
Correct option: B.
$\frac{2}{3} \mathrm{~J}$
(b) $E=\frac{P^2}{2 m}=\frac{4}{2 \times 3}=\frac{2}{3} \mathrm{~J}$
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MCQ 1461 Mark
The potential energy of a weight less spring compressed by a distance a is proportional to
  • A
    $a$
  • $a^2$
  • C
    $a^{-2}$
  • D
    $a^0$
Answer
Correct option: B.
$a^2$
(b) Potential energy of spring $=\frac{1}{2} K x^2$$\therefore P E\propto x^2\Rightarrow P E \propto a^2$
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MCQ 1471 Mark
In an explosion a body breaks up into two pieces of unequal masses. In this
  • Both parts will have numerically equal momentum
  • B
    Lighter part will have more momentum
  • C
    Heavier part will have more momentum
  • D
    Both parts will have equal kinetic energy
Answer
Correct option: A.
Both parts will have numerically equal momentum
(a) Both part will have numerically equal momentum and lighter part will have more velocity.
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MCQ 1481 Mark
A bullet of mass $m$ moving with velocity $v$ strikes a block of mass $M$ at rest and gets embedded into it. The kinetic energy of the composite block will be
  • $\frac{1}{2} m v^2 \times \frac{m}{(m+M)}$
  • B
    $\frac{1}{2} m v^2 \times \frac{M}{(m+M)}$
  • C
    $\frac{1}{2} m v^2 \times \frac{(M+m)}{M}$
  • D
    $\frac{1}{2} M v^2 \times \frac{m}{(m+M)}$
Answer
Correct option: A.
$\frac{1}{2} m v^2 \times \frac{m}{(m+M)}$
(a) By conservation of momentum, $\quad m v+M \times 0=(m+M) V$ Velocity of compositeblock$V=\left(\frac{m}{m+M}\right) v$K.E. of composite block $=\frac{1}{2}(M+m) V^2$$=\frac{1}{2}(M+m)\left(\frac{m}{M+m}\right)^2 v^2=\frac{1}{2} m v^2\left(\frac{m}{m+M}\right)$
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MCQ 1491 Mark
A film of water is formed between two straight parallel wires of length $10 \mathrm{~cm}$ each separated by $0.5 \mathrm{~cm}$. If their separation is increased by $1 \mathrm{~mm}$ while still maintaining their parallelism, how much work will have to be done $\left(\right.$ Surface tension of water $=7.2 \times 10^{-2} \mathrm{~N} / \mathrm{m}$ )
  • A
    $7.22 \times 10^{-6}$ Joule
  • $1.44 \times 10^{-5}$ Joule
  • C
    $2.88 \times 10^{-5}$ Joule
  • D
    $5.76 \times 10^{-5}$ Joule
Answer
Correct option: B.
$1.44 \times 10^{-5}$ Joule
$ \text { Increment in area of soap film }=A_2-A_1 $
$ =2 \times[(10 \times 0.6)-(10 \times 0.5)] \times 10^{-4}=2 \times 10^{-4} \mathrm{~m}^2 $
$ \text { Work done }=T \times \Delta A$
$ =7.2 \times 10^{-2} \times 2 \times 10^{-4}=1.44 \times 10^{-5} \mathrm{~J}$
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MCQ 1501 Mark
If the momentum of a body increases by $0.01 \%$, its kinetic energy will increase by
  • A
    $0.01 \%$
  • $0.02 \%$
  • C
    $0.04 \%$
  • D
    $0.08 \%$
Answer
Correct option: B.
$0.02 \%$
(b) $E \propto P^2$ (if $m=$ constant)Percentage increase in $E=2$ (Percentage increase in $P$ )$=2 \times 0.01 \%=0.02 \%$
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MCQ - Page 3 - JEE physics STD 12 Science Questions - Vidyadip