Centre of Mass & Rotational Motion · JEE Main previous year questions

One solid sphere $A$ and another hollow sphere $B$ are of same mass and same outer radii. Their moment of inertia about their diameters are respectively $I_A$ and $I_B$ such that

1. A.$I_A<I_B$
2. B.$I_A>I_B$
3. C.$I_A=I_B$
4. D.$\frac{I_A}{I_B}=\frac{d_A}{d_B}$ where $d_A$ and $d_B$ are their densities.

Initial angular velocity of a circular disc of mass $M$ is ${\omega }_1$. Then two small spheres of mass $m$ are attached gently to diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?

1. A.$\left(\frac{M+m}{M}\right){\omega }_1$
2. B.$\left(\frac{M+m}{m}\right){\omega }_1$
3. C.$\left(\frac{M}{M+4m}\right){\omega }_1$
4. D.$\left(\frac{M}{M+2m}\right){\omega }_1$

A cylinder of height $20\mathrm{m}$ is completely filled with water. The velocity of efflux of water (in $\mathrm{m}{\mathrm{s}}^{-1}$) through a small hole on the side wall of the cylinder near its bottom is

1. A.$10$
2. B.$20$
3. C.$25.5$
4. D.$5$

Two identical particles move towards each other with velocity $2v$ and $v$ respectively. The velocity of center of mass is

1. A.$v$
2. B.$v/3$
3. C.$v/2$
4. D.zero

A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum acceleration down the plane is for (no rolling)

1. A.solid sphere
2. B.hollow sphere
3. C.ring
4. D.all same

1. A.$mvL$
2. B.$mvl$
3. C.$mvr$
4. D.zero

Moment of inertia of a circular wire of mass $M$ and radius $R$ about its diameter is

1. A.$\frac{M{R}^2}{2}$
2. B.$M{R}^2$
3. C.$2M{R}^2$
4. D.$\frac{M{R}^2}{4}$