JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Rotational Mechanics

A solid sphere (A) of mass, 5 m and spherical shell (B) of mass

m

, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of A and B, they start rolling without slipping with an acceleration of

a_{A}

and

a_{B}

, respectively. The ratio of

a_{A}

and

a_{B}

is ______.

(A) $5 : 21$ ✓ Correct
(B) $6 : 10$
(C) $21 : 25$
(D) $1 : 5$

Answer: (A)

Solution

A horizontal force

F

applied at the top with friction

f

at the contact gives, for rolling without slipping,

F + f = M a

and

F R - f R = I \frac{a}{R}

; eliminating

f

gives

a = \frac{2 F}{M + I / R ^{2}}

. For the solid sphere

M = 5 m

and

I = \frac{2}{5} (5 m) R^{2} = 2 m R^{2}

, so

M + I / R^{2} = 7 m

and

a_{A} = \frac{2 F}{7 m}

. For the shell

M = m

and

I = \frac{2}{3} m R^{2}

, so

M + I / R^{2} = \frac{5 m}{3}

and

a_{B} = \frac{6 F}{5 m}

. The ratio is

\frac{a _{A}}{a _{B}} = \frac{2/7}{6/5} = \frac{5}{21}

, that is

5 : 21

JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Single correct option

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JEE Main · 2026 · 06 Apr 2026 · Shift 2 · Rotational Mechanics

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