CPET Physics Quiz-2 - Ashirbad Mohanty

1. 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

$\frac{5}{9}L$

$\frac{4}{9}L$

$\frac{2}{9}L$

$\frac{1}{9}L$

2. The mass per unit length of a rod (length $2m$) varies as $\rho=3x kg/m$. The moment of inertia (in $kg m^2$) of the rod about a perpendicular axis passing through the tip of the rod (at $x=0$)

3. 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

along $\vec{\omega}$

along $\vec{v}$

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

always directed towards the axis of rotation.

4. The velocity and acceleration of a particle moving in a two dimensional plane with unit vectors $\hat{r}$ and $\hat{\theta}$ in terms of the polar coordinates are

$\dot{r}\hat{r}+r\dot{\theta}\hat{\theta}$ and $(\ddot{r}-r\dot{\theta}^2)\hat{r}+(r \ddot{\theta} + 2\dot{r}\dot{\theta})\hat{\theta}$

$\dot{r}\hat{r}+r\dot{\theta}\hat{\theta}$ and $(\ddot{r}-r\dot{\theta}^2)\hat{r}+(r \dot{\theta} + 2\dot{r}\dot{\theta})\hat{\theta}$

$\dot{r}\hat{r}+r\ddot{\theta}\hat{\theta}$ and $(\ddot{r}-r\dot{\theta}^2)\hat{r}+(r \dot{\theta} + 2\dot{r}\dot{\theta})\hat{\theta}$

$\dot{r}\hat{r}+\dot{r}\dot{\theta}\hat{\theta}$ and $(\ddot{r}-r\dot{\theta}^2)\hat{r}+(r \ddot{\theta} + 2\dot{r}\dot{\theta})\hat{\theta}$

5. A particle of unit mass moves in a potential $V(x)=x^3-3x+2$. The angular frequency of small oscillation about the minimum of potential is

$\sqrt{6}$

$\sqrt{3}$

$\frac{1}{\sqrt{6}}$

$\frac{1}{\sqrt{3}}$

6. With what velocity an electron should move so that its kinetic energy equals its rest mass energy?

$\frac{2}{3} c$

$\frac{\sqrt{3}}{4} c$

$\frac{\sqrt{3}}{2} c$

$\frac{1}{2} c$

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

$\frac{g}{2}$

$\frac{g}{3}$

$\frac{g}{4}$

$2g$

8. Consider a classical particle subjected to an inverse square force field. The total energy of of the particle is $E$ and eccentricity is $\epsilon$. The particle will follow parabolic orbit if

$E>0, \epsilon=1$

$E<0, \epsilon<1$

$E=0, \epsilon=1$

$E<0, \epsilon=1$

9. An electron of rest mass $m_0$ gains energy so that its mass becomes $2m_0$. Its speed is

$\frac{\sqrt{3}}{2} c$

$\frac{3}{2} c$

$\sqrt{\frac{3}{2}} c$

$c$

10. 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

$8T$

$4T$

$T/4$

$T/8$

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

The motion is not restricted to a plane.

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

12. The length of a rod, of length 10m in a frame of reference which is moving with 0.6 c velocity in a direction making 30 degree angle with the rod is

$\sqrt{73} m$

$\sqrt{63} m$

$\sqrt{53} m$

$\sqrt{43} m$

13. Which of the following relations is correct for modulus of rigidity $\eta$ , bulk modulus $K$ and Poisson’s ratio $\sigma$ ?

$\sigma=\frac{K-2\eta}{6K+2\eta}$

$\sigma=\frac{3K-2\eta}{K+2\eta}$

$\sigma=\frac{3K-2\eta}{6K+2\eta}$

$\sigma=\frac{K-2\eta}{K+2\eta}$

14. A solid sphere, a hollow sphere and a disc, all having same mass and radius, are allowed to roll down a rough inclined plane from same height. Which will reach the bottom first ?

solid sphere

hollow sphere

disc

all will reach at the same time

15. A particle moving with relativistic speed $\vec{v}$ has an acceleration $\vec{a}$ due to net force $\vec{F}$. If $m_0$ is the rest mass and $\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$, then net force $\vec{F}$ is

$\frac{m_{0} \vec{a}}{\gamma}$

$\frac{m_{0} \vec{a}}{\gamma^2}$

$\gamma m_0 \vec{a}$

$\gamma^3 m_0 \vec{a}$

16. A particle is kept at rest at a distance R (eart's radius) above the earth's surface. The minimum speed at which it should be projected so that it does not return is

$\sqrt{\frac{GM}{2R}}$

$\sqrt{\frac{2GM}{R}}$

$\sqrt{\frac{GM}{R}}$

$\sqrt{\frac{GM}{4R}}$

17. A spaceship moving away from the earth with velocity $0.5 c$ fires a rocket whose velocity relative to the space is $0.5 c$ away from earth. The velocity of the rocket as observed from the earth is

$c$

$0.1 c$

$0.5 c$

$0.8 c$

18. Air is pushed into a soap bubble of radius $r$ to double its radius. If the surface tension of the soap solution is $S$, the work done in the process is

$4\pi r^2 S$

$8\pi r^2 S$

$16\pi r^2 S$

$24\pi r^2 S$

19. The moment of inertia I of a thin rod of length L and mass M, about an axis perpendicular to the rod at one end, is given by

$\frac{ML^2}{2}$

$\frac{ML^2}{3}$

$\frac{ML^2}{12}$

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

20. A 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

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

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

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

$kA^2$

21. A fluid of coefficient of viscocity $\eta$ is flowing horizontally through a pipe of length $l$ and radius $a$ under a constant pressure difference $p$ over the length of the pipe. The viscous resistance of the fluid is

$\frac{8\eta l}{\pi a^4}$

$\frac{8\eta l}{\pi a^2}$

$\frac{\eta l}{\pi a^4}$

$\frac{\eta l}{\pi a^2}$

22. Which of the following defines a conservative force $\vec{F}$ ?

$\frac{d\vec{F}}{dt}=0$

$\vec{\nabla}\cdot\vec{F}=0$

$\vec{\nabla}\times\vec{F}=0$

$\oint\vec{F}\cdot d\vec{r} \neq 0$

23. A body of mass $M$ rotating in a circular orbit of radius $R$ due to an attractive central force given by $F(r)=-\frac{k}{r}$. Its orbital period would be proportional to

$R^{3/2}$

$R^{1/2}$

$R$

$R^2$

24. The interatomic potential of a diatomic molecule is given by $V(r)=\frac{A}{r^2}-\frac{B}{r}$. The equilibrium separation between the two atoms in the molecule is

$\frac{2A}{B}$

$\frac{A}{2B}$

$\frac{A^2}{2B}$

$\frac{2A^2}{B}$

25. 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

$20 m/s$

$10 m/s$

$5\sqrt{2} m/s$

$5 m/s$