A solid sphere and a hollow sphere of the same mass and of same...

A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be

t_1

and

t_2

, respectively, then

Options

A $t_1\gt t_2$
B $t_1=t_2$
C $t_1 \lt t_2$
D $t_1=2 t_2$

Correct answer

C. $t_1 \lt t_2$

Step-by-step solution

\begin{aligned} & \mathrm{t}=\sqrt{\frac{2 \ell}{\mathrm{a}_{\mathrm{cm}}}} \\ & \mathrm{a}_{\mathrm{cm}}=\frac{\mathrm{g} \sin \theta}{1+\frac{\mathrm{I}_{\mathrm{cm}}}{\mathrm{MR}^2}} \\ & \mathrm{a}_1=\mathrm{a}_{\mathrm{cm}_1}=\frac{5 \mathrm{ g} \sin \theta}{7} \ldots . . \text{ Solid } \\ & \mathrm{a}_2=\mathrm{a}_{\mathrm{cm}_2}=\frac{3 \mathrm{ g} \sin \theta}{5} \ldots . . \text{ Hollow } \\ & \mathrm{a}_1>\mathrm{a}_2 \\ & \mathrm{t}_1 < \mathrm{t}_2\end{aligned}

Practice Rotational Motion on Quantrex Academy →

More from Rotational Motion

Consider a large disk of radius R and two smaller disks, each of radius r = R/50 , lying… JEE Advanced 2026 A solid cylinder of radius R rolls without slipping with a center of mass speed v_0 =… JEE Advanced 2026 List-I shows four planar structures made of uniform solid rods each of mass m and length… JEE Advanced 2026 Passage: A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top… JEE Advanced 2026 Passage: A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top… JEE Advanced 2026 A solid cylinder having radius R and length L is slipping on a rough horizontal plane. At… JEE Main 2026 A solid sphere ( A ) of mass 5m and a spherical shell ( B ) of mass m , both having same… JEE Main 2026 A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through… JEE Main 2026 Full Rotational Motion list All JEE Main PYQs