A particle moves in a circle of radius 5 cm with constant speed and time period 0.2$\pi$s. The acceleration of the particle is

(1) 5 m$s^{-2}$

(2) 15 m$s^{-2}$

(3) 25 m$s^{-2}$

(4) 36 m$s^{-2}$

A planet moving along an elliptical orbit is closest to the sun at a distance $r_1$ and farthest away at a distance of $r_2$. If $v_1<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>v_2$ are the linear velocities at these points respectively. Then the ratio $\frac{v_1}{v_2}$ is

(1) $\frac{r_1}{r_2}$

(2) ${\left(\frac{r_1}{r_2}\right)}^2$

(3) $\frac{r_2}{r_1}$

(4) ${\left(\frac{r_2}{r_1}\right)}^2$

When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

(1) the radius

(2) the tangent to the orbit

(3) a line perpendicular to the plane of rotation

(4) the line making an angle of $45°$ to the plane

Three masses are placed on the x-axis: 300 g at origin, 500 g at x = 40 cm and 400 g  at x = 70 cm.The distance of the center of mass from the origin is

(1) 50 cm

(2) 30 cm

(3) 40 cm

(4) 45 cm

A rod of weight W  supported by two parallel knife edges A and B is in equilibrium in a horizontal position. The knives are at a distance d from each other. The center of mass of the rod is at distance x from A. The normal reaction on A is

(1) $\frac{Wd}{x}$

(2) $\frac{W(d-x)}{x}$

(3) $\frac{W(d-x)}{d}$

(4) $\frac{Wx}{d}$

Four identical thin rods each of mass M and length l, from a square frame. Moment of inertia of this frame about an axis through the center of the square and perpendicular to its plane is -

(1) $\frac{2}{3}M{I}^2$

(2) $\frac{13}{3}M{I}^2$

(3) $\frac{1}{3}M{I}^2$

(4) $\frac{4}{3}M{I}^2$

A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane and passing through its center with a constant angular velocity $\omega$. If objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity

(1) $\frac{\omega M}{M+2m}$

(2) $\frac{\omega (M+2m)}{M}$

(3) $\frac{\omega M}{M+m}$

(4) $\frac{\omega (M-2m)}{M+2m}$

The moment of inertia of a uniform circular disc is maximum about an axis perpendicular to the disc and passing through

(1) D

(2) A

(3) B

(4) C

Two bodies of mass 1 kg and 3 kg have position vectors $\hat{i}+2\hat{j}+\hat{k}<mspace\; width="1em"></mspace>and<mspace\; width="1em"></mspace>-3\hat{i}-2\hat{j}+\hat{k}$ respectively. The center of mass of this system has a position vector

(1) $-2\hat{i}-\hat{j}+\hat{k}$

(2) $2\hat{i}-\hat{j}-\hat{k}$

(3) $-\hat{i}+\hat{j}+\hat{k}$

(4) $-2\hat{i}+2\hat{k}$

A wheel has angular acceleration of 3.0 rad $s^{-2}$ and an initial angular speed of 2.00 rad $s^{-1}$. In a time 2 s it has rotated through an angle (in radian) of

(1) 10 

(2) 12

(3) 4

(4) 6