A solid sphere (A) of mass 5m and a spherical shell (B) of mass m… | JEE Main 2026 (6 Apr, Shift 2)

Q8JEE Main 2026 · 6 APR · SHIFT 2Medium

Rolling Motion

A solid sphere $(A)$ of mass $5m$ and a 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 ______.

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Answer: (a)

Force $F$ at top, friction $f$ forward at bottom, $I = kMR^2$ : $F + f = Ma$ and $(F - f)R = kMR^2\dfrac{a}{R}$ .
Adding: $2F = (1+k)Ma \Rightarrow a = \dfrac{2F}{(1+k)M}$ .
Sphere A ( $k = \frac{2}{5}$ , mass $5m$ ): $a_A = \dfrac{2F}{7m}$ . Shell B ( $k = \frac{2}{3}$ , mass $m$ ): $a_B = \dfrac{6F}{5m}$ .
$\dfrac{a_A}{a_B} = \dfrac{2}{7}\times\dfrac{5}{6} = \dfrac{5}{21}$ .
So the answer is (a) $5 : 21$ .

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