Q: A force of 10 N acts at 60^\circ to the direction of a 4 m displacement. The work done is

20 J. W = Fd\cos\theta = 10\times4\times\cos 60^\circ = 20 J.

Q: A particle rotates with angular velocity \omega = 2 rad/s at position r = 3 m perpendicular to the rotation axis. Its speed |\vec v| = |\vec\omega\times\vec r| is

6 m/s. v = \omega r\sin 90^\circ = 2\times3 = 6 m/s.

Q: For unit vectors \hat{p} and \hat{q}, \hat{p}\cdot\hat{q} equals

\cos\theta, where \theta is the angle between them. \hat{p}\cdot\hat{q} = (1)(1)\cos\theta = \cos\theta.

Question 1

The value of \lambda for which \vec A = \lambda\hat{i} + \hat{j} is perpendicular to \vec B = \hat{i} - \hat{j} is

Accepted Answer

1. \vec A\cdot\vec B = \lambda - 1 = 0 \Rightarrow \lambda = 1.

Question 2

A body of mass 0.5 kg has momentum \vec p = (3\hat{i} + 4\hat{j}) kg·m/s. Its kinetic energy is

Accepted Answer

25 J. p^2 = \vec p\cdot\vec p = 9+16 = 25; KE = \frac{p^2}{2m} = \frac{25}{1} = 25 J.

Question 3

Forces \vec F_1 = \hat{i}+\hat{j} N and \vec F_2 = 2\hat{i}-\hat{j} N act on a body displaced by \vec d = 3\hat{i} m. The total work done is

Accepted Answer

9 J. Net force = 3\hat{i} N; W = (3\hat{i})\cdot(3\hat{i}) = 9 J.

Question 4

\vec B is parallel to \vec A = 4\hat{i} + 3\hat{j} and |\vec B| = 10. Then \vec B is

Accepted Answer

8\hat{i} + 6\hat{j}. \hat{A} = \frac{4\hat{i}+3\hat{j}}{5}; \vec B = 10\hat{A} = 8\hat{i}+6\hat{j}.

Question 5

A force of 10 N acts at 60^\circ to the direction of a 4 m displacement. The work done is

Accepted Answer

20 J. W = Fd\cos	heta = 10	imes4	imes\cos 60^\circ = 20 J.

Question 6

A particle rotates with angular velocity \omega = 2 rad/s at position r = 3 m perpendicular to the rotation axis. Its speed |\vec v| = |\vec\omega	imes\vec r| is

Accepted Answer

6 m/s. v = \omega r\sin 90^\circ = 2	imes3 = 6 m/s.

Question 7

What vector must be added to \hat{i} + 2\hat{j} to get a resultant of 3\hat{i}?

Accepted Answer

2\hat{i} - 2\hat{j}. Required vector = 3\hat{i} - (\hat{i}+2\hat{j}) = 2\hat{i} - 2\hat{j}.

Question 8

The vectors \vec A = \hat{i} + \hat{j} - 2\hat{k} and \vec B = 2\hat{i} - 2\hat{j} are

Accepted Answer

Perpendicular. \vec A\cdot\vec B = (1)(2) + (1)(-2) + (-2)(0) = 0 — perpendicular.

Question 9

For unit vectors \hat{p} and \hat{q}, \hat{p}\cdot\hat{q} equals

Accepted Answer

\cos	heta, where 	heta is the angle between them. \hat{p}\cdot\hat{q} = (1)(1)\cos	heta = \cos	heta.

Question 10

If (\vec a + \vec b)\cdot(\vec a + \vec b) = a^2 + b^2, then \vec a and \vec b are

Accepted Answer

Perpendicular. Expanding gives a^2 + b^2 + 2\vec a\cdot\vec b; equality forces \vec a\cdot\vec b = 0.

Question 11

For a line making angles \alpha, \beta, \gamma with the coordinate axes, \sin^2\alpha + \sin^2\beta + \sin^2\gamma equals

Accepted Answer

2. \sum\sin^2 = \sum(1 - \cos^2) = 3 - 1 = 2.

Question 12

Can a line make angles 30^\circ, 45^\circ and 60^\circ with the x, y and z axes respectively?

Accepted Answer

No, because \cos^2 30^\circ + \cos^2 45^\circ + \cos^2 60^\circ 
eq 1. \frac{3}{4} + \frac{1}{2} + \frac{1}{4} = \frac{3}{2} 
eq 1 — such a line cannot exist.

Question 13

If a vector makes \gamma = 90^\circ with the z-axis, the vector lies

Accepted Answer

In the xy-plane. n = \cos 90^\circ = 0 means no z-component — the vector lies entirely in the xy-plane.

Question 14

There are two force vectors, one of 5 N and other of 12 N. If the resultant of the two forces has a magnitude of 17 N, 7 N and 13 N respectively, at what angle the two vectors be added to get these resultants?

Accepted Answer

0°, 180° and 90°. For resultant = 17 N (max), angle = 0°. For resultant = 7 N (min), angle = 180°. For resultant = 13 N, angle = 90°.

Question 15

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

Accepted Answer

0°. Resultant is maximum when vectors are parallel (angle = 0°).

Question 16

A particle is simultaneously acted by two forces equal to 4 N and 3 N. The net force on the particle is

Accepted Answer

Between 1 N and 7 N. Resultant can vary from |4-3| = 1 N to 4+3 = 7 N depending on angle.

Question 17

Forces \vec{F}_1 and \vec{F}_2 act on a point mass in two mutually perpendicular directions. The resultant force on the point mass will be

Accepted Answer

\sqrt{F_1^2 + F_2^2}. For perpendicular forces, resultant = \sqrt{F_1^2 + F_2^2} (Pythagorean theorem).

Question 18

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

Accepted Answer

0°. This equality holds only when vectors are parallel (0° angle).

Question 19

The magnitude of vectors \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

Accepted Answer

90°. Since 12^2 + 5^2 = 13^2 (144 + 25 = 169), vectors are perpendicular.

Question 20

Magnitude of vector which comes on addition of two vectors, 6\hat{i} + 7\hat{j} and 3\hat{i} + 4\hat{j} is

Accepted Answer

\sqrt{202}. Sum = 9\hat{i} + 11\hat{j}. Magnitude = \sqrt{81 + 121} = \sqrt{202}.

Vectors — NEET Physics MCQs with Solutions

Subtopics

Sample questions with solutions