CUET PG 2023 Physics Part Test-2: Mechanics

1. A particle stays at rest as seen in a frame. We can conclude that

A. The frame is inertial.

B. Resultant force on the particle is zero.

C. The may frame may be inertial but the resultant force on the particle is zero

D. The frame may be nonoinertial but there is a nonzero resultant force.

Choose the most appropriate answer from the option given below:

C, D

A, C

A, B

B, C

2. A cylindrical rod of length $L$ has a mass density distribution given by $\rho(x)=\rho_0(1+\frac{x}{L})$, where $x$ is measured from one end of the rod and $\rho_0$is a constant of appropriate dimensions. The center of mass of the rod is

$\frac{5}{9}L$

$\frac{4}{9}L$

$\frac{2}{9}L$

$\frac{1}{9}L$

3. When a particle moves in a circle with a uniform speed

its velocity and acceleration both change

its velocity and acceleration both are constant

its velocity is constant but acceleration changes

its acceleration is constant but velocity changes

4. A uniform disk of mass $m$ and radius $R$ rolls, without slipping, down a fixed plane inclined at an angle $30^0$ to the horizontal. The linear acceleration of the disk is

$\frac{g}{3}$

$\frac{g}{2}$

$\frac{g}{4}$

$2g$

5. A satellite moves around a planet in a circular orbit at a distance $R$ from its center. The time period of revolution of the satellite is $T$. If the same satellite is taken to an orbit of radius $4R$ around the same planet, the time period would be

$8T$

$4T$

$T/4$

$T/8$

6. A particle is moving in a plane with constant radial velocity of $12 m/s$ and constant angular velocity of $2 rad/s$. When the particle is at a distance $r=8 m$ from the origin, the magnitude of instantaneous velocity of the particle is

$20 m/s$

$10 m/s$

$5\sqrt{2} m/s$

$5 m/s$

7. The total work done on a particle is equal to the change in its kinetic energy

always

only if the the forces are conservative

only if gravitational force alone acts on it

only if elastic force alone acts on it

8. Consider an object moving with a velocity $\vec{v}$ in a frame which rotates with a constant angular velocity $\vec{\omega}$. The Coriolis force experienced by the object is

perpendicular to both Perpendicular to both $\vec{v}$ and $\vec{\omega}$

along $\vec{\omega}$

along $\vec{v}$

always directed towards the axis of rotation.

9. Consider the following two statements:

Statement I: The linear momentum of a particle is independent of the frame of reference.

Statement II: The kinetic energy of a particle is independent of the frame of reference.

In the light of the above statements, choose the most appropriate answer from the options given below:

both statement I and statement II are incorrect.

both statement I and statement II are correct

statement I is correct but statement II is incorrect

statement I is incorrect but statement II is correct.

10. For a particle moving in a central potential, which one of the following statements are correct?

The motion is restricted to a plane due to the conservation of angular momentum.

The motion is restricted to a plane due to the conservation of energy only.

The motion is restricted to a plane due to the conservation of linear momentum.

The motion is not restricted to a plane.

11. Two objects of masses $m$ and $2m$ are moving at speeds of $v$ and $v/2$ , respectively. After undergoing a completely inelastic collision, they move together with a speed of $v/3$ . The angle between the initial velocity of the two objects is

$120\textdegree$

$60\textdegree$

$30\textdegree$

$45\textdegree$

12. The moment of inertia of a solid sphere of radius $R$ and mass $M$ about the axis which is at a distance of $\frac{R}{2}$ from the centre is

$\frac{13}{20}MR^2$

$\frac{13}{10}MR^2$

$\frac{3}{20}MR^2$

$\frac{3}{10}MR^2$

13. The time period of a simple pendulum inside a stationary lift is $T$ seconds. If the lift accelerates upward with an acceleration $g/4$, then the time period will be

$\frac{2T}{\sqrt{5}}$

$\frac{2T}{\sqrt{10}}$

$\frac{2T}{5}$

$\frac{T}{5}$

14. In an inelasic collision

A. the kinetic energy remains constant.

B. the linear momentum remains constant.

C. the final kinetic energy is equal to the initial kinetic energy.

D. the final kinetic energy is less than the intial kinetic energy.

Choose the most appropriate answer from the options given below:

B, D

A, B

15. A hollow sphere and a solid sphere having same mass and same radii are rolled down a rough inclined plane. If the spheres roll without slipping,

A. the solid sphere reaches the bottom with greater speed.

B. the solid sphere reaches the bottom with greater kinetic energy.

C. the hollow sphere reaches the bottom with greater speed.

D. the two spheres will reach the bottom with same linear momentum.

Choose the most appropriate answer from the options given below:

B, D

B, C

16. A projectile of mass m, fired from the earth's surface along a direction making 45° with the vertical, is seen to reach a maximum vertical height in two seconds and subsequently reaches the earth's surface. The ratio of the horizontal distance traveled to the maximum vertical height reached, is

1/2

1/4

17. A body of mass $m$ connected to a spring of force constant $k$ is stretched by a length $A$ and then released from rest so that it executes simple harmonic motion. The average kinetic energy, averaged over one time period, is

$\frac{kA^2}{4}$

$\frac{kA^2}{2}$

$\frac{kA^2}{4m}$

$\frac{kA^2}{2m}$

18. A thick viscous liquid is flowing through a horizontal tube due to a constant pressure difference between the ends. If the radius of the tube is doubled and the length is reduced to half, then the volume rate of the liquid flow

increases by 32 times

increases by 8 times

decreases by 16 times

remains constant

19. The rotational kinetic energy of a thin disk, of mass $20 kg$ and radius $70 cm$, rotating like a merry-go-round at an angular speed of $120 radians/min$, is

$9.8 J$

$5.9 J$

$21.6 J$

$4.9 J$

20. Let $V$ and $E$ be the gravitational potential and field at a distance $r$ from the centre of a uniform spherical shell. Consider the following two statements:

Statement I: The plot of $V$ against $r$ is discontinuous.

Statement II: The plot of $E$ against $r$ is discontinuous.

In the light of the above statements, choose the most appropriate answer from the options given below:

Statement I is incorrect but Statement II is correct.

Statement I is correct but Statement II is incorrect.

Both statement I and statement II are correct.

Both statement I and statement II are incorrect.

21. Bernoulli theorem is based on conservation of

energy

momentum

mass

angular momentum

22. Let $(r,\theta)$ denote the polar coordinates of a particle moving in a plane. If $\hat{r}$ and $\hat{\theta}$ represent the corresponding unit vectors, then

A. $\frac{d\hat{r}}{d\theta}=\hat{\theta}$

B. $\frac{d\hat{r}}{d R}=-\hat{\theta}$

C. $\frac{d \hat{\theta}}{d \theta}=-\hat{r}$

D. $\frac{d \hat{\theta}}{d R}=\hat{r}$

Choose the correct answer from the options given below.

A, C

B, D

A, B

C, D

23. A particle of mass $m$ and angular momentum $L$ moves in space where its potential energy is $U(r)=kr^2 (k>0)$ and $r$ is the radial coordinate. If the particle moves in a circular orbit, then the radius of the orbit is

$(\frac{L^2}{2mk})^{1/4}$

$(\frac{L^2}{mk})^{1/4}$

$(\frac{2L^2}{mk})^{1/4}$

$(\frac{4L^2}{mk})^{1/4}$

24. In a streamline flow,

A. the speed of the particle always remains same.

B. the velocity of the particle always remain same.

C. the kinetic energies of all the particles arriving at a given point are the same.

D. the momenta of all the particles arriving at a given point are the same.

Choose the correct answer from the options given below:

C, D

B, C

A, B

25. Consider a planet which has a mass double the mass of the earth and density equal to density of earth. An object weighing $W$ on the earth will weigh

$2^{1/3}W$

$W$

$W/2$

$2W$