A particle is projected vertically upwards from O with velocity v… - Vidyadip

MCQ

A particle is projected vertically upwards from $O$ with velocity $v$ and a second particle is projected at the same instant from $P$ (at a height h above $O$) with velocity $v$ at an angle of projection $\theta$ . The time when the distance between them is minimum is

A
$\frac{h}{{2v\sin \,\theta }}$
B
$\frac{h}{{2v\cos \,\theta }}$
C
$h/v$
✓
$h/2v$

✓

Answer

Correct option: D.

$h/2v$

d
In from of ball thrown from $p$

$v_{\text {resultant }}=2 v \cos \left(\frac{90^{\circ}+\theta}{2}\right)$

$=2 v \cos \left(45^{\circ}+\theta / 2\right)$

$t=\frac{d}{v_{\text {resultant }}}=\frac{h \cos \left(45^{\circ}+\frac{\theta}{2}\right)}{2 v \cos \left(45^{\circ}+\frac{\theta}{2}\right)}=\frac{h}{2 v}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 3.2 , motion in plane→3.2 , motion in plane — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The thermodynamic process, in which internal energy of the system remains constant is ...........

A rod of length $L$ at room temperature and uniform area of cross section $A$, is made of a metal having coefficient of linear expansion $\alpha {/^o}C$. It is observed that an external compressive force $F$, is applied on each of its ends, prevents any change in the length of the rod, when it temperature rises by $\Delta \,TK$. Young’s modulus, $Y$, for this metal is

When a $1.0\,kg$ mass hangs attached to a spring of length $50 cm$, the spring stretches by $2 \,cm$. The mass is pulled down until the length of the spring becomes $60\, cm.$ What is the amount of elastic energy stored in the spring in this condition, if $g = 10 m/s^{2}$ ............. $\mathrm{Joule}$

A mass of $10\; kg$ is suspended by a rope of length $4 \;\mathrm{m},$ from the ceiling. A force $\mathrm{F}$ is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of $45^{\circ}$ with the vertical. Then $\mathrm{F}$ equals ........... $N$

(Take $\mathrm{g}=10 \;\mathrm{ms}^{-2}$ and the rope to be massless)

In the relation $P = \frac{\alpha }{\beta }{e^{ - \frac{{\alpha Z}}{{k\theta }}}}$ $P$ is pressure, $Z$ is the distance, $k$ is Boltzmann constant and $\theta$ is the temperature. The dimensional formula of $\beta$ will be

A body of mass $2\, kg$ moves under a force of $(2 \hat{ i }+3 \hat{ j }+5 \hat{ k }) \,N$. It starts from rest and was at the origin initially. After $4 \,s$, its new coordinates are $(8, b, 20)$. The value of $b$ is ........ . (Round off to the Nearest Integer)

A bullet of mass $10\, g$ moving horizontally with a velocity of $400\, m s^{-1}$ strikes a wood block of mass $2\, kg$ which is suspended by light inextensible string of length $5\, m.$ As a result, the centre of gravity of the block found to rise a vertical distance of $10\, cm.$ The speed of the bullet after it emerges out horizontally from the block will be ................... $\mathrm{ms}^{-1}$

In the figure, a ladder of mass $m$ is shown leaning against a wall. It is in static equilibrium making an angle $\theta$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $\mu_1$ and that between the floor and the ladder is $\mu_2$. The normal reaction of the wall on the ladder is $N_1$ and that of the floor is $N_2$. If the ladder is about to slip, then

$Image$

$(A)$ $\mu_1=0 \mu_2 \neq 0$ and $N _2 \tan \theta=\frac{ mg }{2}$

$(B)$ $\mu_1 \neq 0 \mu_2=0$ and $N_1 \tan \theta=\frac{m g}{2}$

$(C)$ $\mu_1 \neq 0 \mu_2 \neq 0$ and $N _2 \tan \theta=\frac{ mg }{1+\mu_1 \mu_2}$

$(D)$ $\mu_1=0 \mu_2 \neq 0$ and $N _1 \tan \theta=\frac{ mg }{2}$

The velocity of a particle moving on the $x-$ axis is given by $v = x^2 + x$ where $v$ is in $m/s$ and $x$ is in $m$ . Find its acceleration in $m/s^2$ when passing through the point $x = 2m$

A wire is suspended from the ceiling and stretched under the action of a weight $F$ suspended from its other end. The force exerted by the ceiling on it is equal and opposite to the weight.