MCQ

MCQ 1511 Mark

A metal sphere is hung by a string fixed to a wall. The sphere is pushed away from the wall by a stick. The forces acting on the sphere are shown in the second diagram. Which of the following statements is wrong

A
$P=W \tan \theta$
B
$\vec{T}+\vec{P}+\vec{W}=0$
C
$T^2=P^2+W^2$
✓
$T=P+W$

Answer

Correct option: D.

$T=P+W$

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MCQ 1521 Mark

Find the resultant of three vectors $\overrightarrow{O A}, \overrightarrow{O B}$ and $\overrightarrow{O C}$ shown in the following figure. Radius of the circle is $R$.

A
$2 R$
✓
$R(1+\sqrt{2})$
C
$R \sqrt{2}$
D
$\quad R(\sqrt{2}-1)$

Answer

Correct option: B.

$R(1+\sqrt{2})$

(b) $R_{\text {net }}=R+\sqrt{R^2+R^2}=R+\sqrt{2} R=R(\sqrt{2}+1)$

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MCQ 1531 Mark

A vector $\vec{a}$ is turned without a change in its length through a small angle $d \theta$. The value of $|\Delta \vec{a}|$ and $\Delta a$ are respectively

A
$0, \operatorname{ad\theta }$
✓
$\operatorname{ad} \theta, 0$
C
0,0
D
None of these

Answer

Correct option: B.

$\operatorname{ad} \theta, 0$

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MCQ 1541 Mark

If a vector $\vec{P}$ making angles $\alpha, \beta$, and $\gamma$ respectively with the $X, \gamma$ and $Z$ axes respectively. Then $\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma=$

B
1
✓
2
D
3

Answer

Correct option: C.

(c) \sin ^2 \alpha+\sin ^2 \beta+\sin \gamma \\& =1-\cos ^2 \alpha+1-\cos ^2 \beta+1-\cos ^2 \gamma \\& =3-\left(\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma\right)=3-1=2\end{aligned}$

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MCQ 1551 Mark

Two equal forces ( $P$ each) act at a point inclined to each other at an angle of $120^{\circ}$. The magnitude of their resultant is

A
$P / 2$
B
$P / 4$
✓
$P$
D
$2 P$

Answer

Correct option: C.

$P$

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MCQ 1561 Mark

$y$ component of velocity is 20 and $x$ component of velocity is 10 . The direction of motion of the body with the horizontal at this instant is

✓
$\tan ^{-1}(2)$
B
$\tan ^{-1}(1 / 2)$
C
$45^{\circ}$
D
$0^{\circ}$

Answer

Correct option: A.

$\tan ^{-1}(2)$

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MCQ 1571 Mark

What displacement must be added to the displacement $25 \hat{i}-6 \hat{j} m$ to give a displacement of $7.0 m$ pointing in the $x$ direction

A
$18 \hat{i}-6 \hat{j}$
B
$32 \hat{i}-13 \hat{j}$
✓
$-18 \hat{i}+6 \hat{j}$
D
$-25 \hat{i}+13 \hat{j}$

Answer

Correct option: C.

$-18 \hat{i}+6 \hat{j}$

(c)

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MCQ 1581 Mark

Given that $\vec{A}+\vec{B}=\vec{C}$ and that $\vec{C}$ is $\perp$ to $\vec{A}$. Further if $|\vec{A}|=|\vec{C}|$, then what is the angle between $\vec{A}$ and $\vec{B}$

A
$\frac{\pi}{4}$ radian
B
$\frac{\pi}{2}$ radian
✓
$\frac{3 \pi}{4}$ radian
D
$\pi$ radian

Answer

Correct option: C.

$\frac{3 \pi}{4}$ radian

(c)

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MCQ 1591 Mark

Two forces, $F_1$ and $F_2$ are acting on a body. One force is double that of the other force and the resultant is equal to the greater force. Then the angle between the two forces is

A
$\cos ^{-1}(1 / 2)$
B
$\cos ^{-1}(-1 / 2)$
✓
$\cos ^{-1}(-1 / 4)$
D
$\cos ^{-1}(1 / 4)$

Answer

Correct option: C.

$\cos ^{-1}(-1 / 4)$

(c)

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MCQ 1601 Mark

The resultant of two vectors $\vec{P}$ and $\vec{Q}$ is $\vec{R}$. If $Q$ is doubled, the new resultant is perpendicular to $P$. Then $R$ equals

A
$P$
B
$(P+Q)$
✓
$Q$
D
$(P-Q)$

Answer

Correct option: C.

$Q$

(c)

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MCQ 1611 Mark

Maximum and minimum magnitudes of the resultant of two vectors of magnitudes $P$ and $Q$ are in the ratio $3: 1$. Which of the following relations is true

✓
$P=2 Q$
B
$P=Q$
C
$P Q=1$
D
None of these

Answer

Correct option: A.

$P=2 Q$

(a) According to problem $P+Q=3$ and $P-Q=1$By solving we get $P=2$ and $Q=1 \therefore \quad \frac{P}{Q}=2 \Rightarrow P=2 Q$

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MCQ 1621 Mark

The resultant of $\vec{P}$ and $\vec{Q}$ is perpendicular to $\vec{P}$. What is the angle between $\vec{P}$ and $\vec{Q}$

A
$\cos ^{-1}(P / Q)$
✓
$\cos ^{-1}(-P / Q)$
C
$\sin ^{-1}(P / Q)$
D
$\sin ^{-1}(-P / Q)$

Answer

Correct option: B.

$\cos ^{-1}(-P / Q)$

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MCQ 1631 Mark

What is the angle between $\vec{P}$ and the resultant of $(\vec{P}+\vec{Q})$ and $(\vec{P}-\vec{Q})$

✓
Zero
B
$\tan ^{-1}(P / Q)$
C
$\tan ^{-1}(Q / P)$
D
$\tan ^{-1}(P-Q) /(P+Q)$

Answer

Correct option: A.

Zero

(a) Resultant $\vec{R}=\vec{P}+\vec{Q}+\vec{P}-\vec{Q}=2 \vec{P}$ The angle between $\vec{P}$ and $2 \vec{P}$ is zero.

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MCQ 1641 Mark

The resultant of two vectors $A$ and $B$ is perpendicular to the vector $A$ and its magnitude is equal to half the magnitude of vector $B$. The angle between $A$ and $B$ is

A
$120^{\circ}$
✓
$150^{\circ}$
C
$135^{\circ}$
D
None of these

Answer

Correct option: B.

$150^{\circ}$

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MCQ 1651 Mark

When three forces of $50 N , 30 N$ and $15 N$ act on a body, then the body is

A
At rest
B
Moving with a uniform velocity
C
In equilibrium
✓
Moving with an acceleration

Answer

Correct option: D.

Moving with an acceleration

(d) Here all the three force will not keep the particle in equilibrium so the net force will not be zero and the particle will move with an acceleration.

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MCQ 1661 Mark

Let $\vec{C}=\vec{A}+\vec{B}$ then

A
$|\vec{C}|$ is always greater then $|\vec{A}|$
✓
It is possible to have $|\vec{C}|<|\vec{A}|$ and $|\vec{C}|<\vec{B} \mid$
C
$C$ is always equal to $A+B$
D
$C$ is never equal to $A+B$

Answer

Correct option: B.

It is possible to have $|\vec{C}|<|\vec{A}|$ and $|\vec{C}|<\vec{B} \mid$

(b) $\vec{C}+\vec{A}=\vec{B}$.The value of $C$ lies between $A-B$ and $A+B$$\therefore|\vec{C}|<|\vec{A}| \text { or }|\vec{C}|<|\vec{B}|$

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MCQ 1671 Mark

The three vectors $\vec{A}=3 \hat{i}-2 \hat{j}+\hat{k}, \vec{B}=\hat{i}-3 \hat{j}+5 \hat{k} \quad$ and $\vec{C}=2 \hat{i}+\hat{j}-4 \hat{k}$ form

A
An equilateral triangle
B
Isosceles triangle
✓
A right angled triangle
D
No triangle

Answer

Correct option: C.

A right angled triangle

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MCQ 1681 Mark

A particle has displacement of $12 m$ towards east and $5 m$ towards north then $6 m$ vertically upward. The sum of these displacements is

A
12
B
$10.04 m$
✓
$14.31 m$
D
None of these

Answer

Correct option: C.

$14.31 m$

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MCQ 1691 Mark

The magnitude of vector $\vec{A}, \vec{B}$ and $\vec{C}$ are respectively 12,5 and 13 units and $\vec{A}+\vec{B}=\vec{C}$ then the angle between $\vec{A}$ and $\vec{B}$ is

B
$\pi$
✓
$\pi / 2$
D
$\pi / 4$

Answer

Correct option: C.

$\pi / 2$

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MCQ 1701 Mark

Let the angle between two nonzero vectors $\vec{A}$ and $\vec{B}$ be $120^{\circ}$ and resultant be $\vec{C}$

A
$\vec{C}$ must be equal to $|\vec{A}-\vec{B}|$
B
$\vec{C}$ must be less than $|\vec{A}-\vec{B}|$
✓
$\vec{C}$ must be greater than $|\vec{A}-\vec{B}|$
D
$\vec{C}$ may be equal to $|\vec{A}-\vec{B}|$

Answer

Correct option: C.

$\vec{C}$ must be greater than $|\vec{A}-\vec{B}|$

(c)

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MCQ 1711 Mark

If $|\vec{A}-\vec{B}|=|\vec{A}|=|\vec{B}|$, the angle between $\vec{A}$ and $\vec{B}$ is

✓
$60^{\circ}$
B
$0^{\circ}$
C
$120^{\circ}$
D
$90^{\circ}$

Answer

Correct option: A.

$60^{\circ}$

(a)

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MCQ 1721 Mark

If the resultant of the two forces has a magnitude smaller than the magnitude of larger force, the two forces must be

A
Different both in magnitude and direction
B
Mutually perpendicular to one another
C
Possess extremely small magnitude
✓
Point in opposite directions

Answer

Correct option: D.

Point in opposite directions

(d)

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MCQ 1731 Mark

Two vectors $\vec{A}$ and $\vec{B}$ lie in a plane, another vector $\vec{C}$ lies outside this plane, then the resultant of these three vectors i.e., $\vec{A}+\vec{B}+\vec{C}$

A
Can be zero
✓
Cannot be zero
C
Lies in the plane containing $\vec{A}+\vec{B}$
D
Lies in the plane containing $\vec{C}$

Answer

Correct option: B.

Cannot be zero

(b) If $\vec{C}$ lies outside the plane then resultant force can not be zero.

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MCQ 1741 Mark

For the resultant of the two vectors to be maximum, what must be the angle between them

✓
$0^{\circ}$
B
$60^{\circ}$
C
$90^{\circ}$
D
$180^{\circ}$

Answer

Correct option: A.

$0^{\circ}$

(a)

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MCQ 1751 Mark

An object of $m kg$ with speed of $v m / s$ strikes a wall at an angle $\theta$ and rebounds at the same speed and same angle. The magnitude of the change in momentum of the object will be

✓
$2 m v \cos \theta$
B
$2 m v \sin \theta$
C
$2 m v$

Answer

Correct option: A.

$2 m v \cos \theta$

(a)$\begin{aligned}& \vec{P}_1=m v \sin \theta \hat{i}-m v \cos \theta \hat{j} \\& \text { and } \vec{P}_2=m v \sin \theta \hat{i}+m v \cos \theta \hat{j}\end{aligned}$So change in momentum$\overrightarrow{\Delta P}=\vec{P}_2-\vec{P}_1=2 m v \cos \theta \hat{j},\Delta \vec{P}|=2 m v \cos \theta$

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MCQ 1761 Mark

$\vec{A}=2 \hat{i}+\hat{j}, B=3 \hat{j}-\hat{k}$ and $\vec{C}=6 \hat{i}-2 \hat{k}$ Value of $\vec{A}-2 \vec{B}+3 \vec{C}$ would be

A
$20 \hat{i}+5 \hat{j}+4 \hat{k}$
✓
$20 \hat{i}-5 \hat{j}-4 \hat{k}$
C
$4 \hat{i}+5 \hat{j}+20 \hat{k}$
D
$5 \hat{i}+4 \hat{j}+10 \hat{k}$

Answer

Correct option: B.

$20 \hat{i}-5 \hat{j}-4 \hat{k}$

(b)$\begin{aligned}& \vec{A}-2 \vec{B}+3 \vec{C}=(2 \hat{i}+\hat{j})-2(3 \hat{j}\hat{k})+3(6 \hat{i}-2 \hat{k}) \\& =2 \hat{i}+\hat{j}-6 \hat{j}+2 \hat{k}+18 \hat{i}-6 \hat{k}=20 \hat{i}-5 \hat{j}-4 \hat{k}\end{aligned}$

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MCQ 1771 Mark

If $\vec{A}=4 \hat{i}-3 \hat{j}$ and $\vec{B}=6 \hat{i}+8 \hat{j}$ then magnitude and direction of $\vec{A}+\vec{B}$ will be

A
$5, \tan ^{-1}(3 / 4)$
✓
$5 \sqrt{5}, \tan ^{-1}(1 / 2)$
C
$10, \tan ^{-1}(5)$
D
$25, \tan ^{-1}(3 / 4)$

Answer

Correct option: B.

$5 \sqrt{5}, \tan ^{-1}(1 / 2)$

(b) $\begin{aligned} & \vec{A}+\vec{B}=4 \hat{i}-3 \hat{j}+6 \hat{i}+8 \hat{j}=10 \hat{i}+5 \hat{j} \\ & |\vec{A}+\vec{B}|=\sqrt{(10)^2+(5)^2}=5 \sqrt{5} \\ & \tan \theta=\frac{5}{10}=\frac{1}{2} \Rightarrow \theta=\tan ^{-1}\left(\frac{1}{2}\right)\end{aligned}$

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MCQ 1781 Mark

There are two force vectors, one of $5 N$ and other of $12 N$ at what angle the two vectors be added to get resultant vector of $17 N , 7 N$ and $13 N$ respectively

✓
$0^{\circ}, 180^{\circ}$ and $90^{\circ}$
B
$0^{\circ}, 90^{\circ}$ and $180^{\circ}$
C
$0^{\circ}, 90^{\circ}$ and $90^{\circ}$
D
$180^{\circ}, 0^{\circ}$ and $90^{\circ}$

Answer

Correct option: A.

$0^{\circ}, 180^{\circ}$ and $90^{\circ}$

(a) For $17 N$ both the vector should be parallel i.e. angle between them should be zero.For $7 N$ both the vectors should be antiparallel i.e. angle between them should be $180^{\circ}$For $13 N$ both the vectors should be perpendicular to each other i.e. angle between them should be $90^{\circ}$

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JEE physics MCQ