A sphere of mass 2kg and radius 0 . 5m is rolling with an initial...

A sphere of mass $2kg$ and radius $0 . 5m$ is rolling with an initial speed of $1{ms}^{- 1}$ goes up an inclined plane which makes an angle of $30 °$ with the horizontal plane, without slipping. How low will the sphere take to return to the starting point $A$ ?

A sphere of mass 2kg and radius 0 . 5m is rolling with an initial speed of 1 ms ^ - 1 goes up an inclined plane which

Options

A $0 . 60s$
B $0 . 52s$
C $0 . 56s$
D $0 . 80s$

Correct answer

C. $0 . 56s$

Step-by-step solution

$a = \dfrac{gsin\theta}{1 + \dfrac{I}{m{R}^{2}}} = \dfrac{5}{7} \times \dfrac{10}{2} = \dfrac{25}{7}$

$t = \dfrac{2{v}_{0}}{a} = \dfrac{2 \times 1 \times 7}{25}$ $= 0 . 56$ .

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