A solid sphere (A) of mass 5m and spherical shell (B) of mass m, both having same radius, are placed on a rough surface

Question

A solid sphere (A) of mass 5m 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 ________. [2026]

Smart Achievers · Accepted Answer

(1)

$τ_{p} = I_{p} α \Rightarrow F (2 R) = I \frac{a}{R}$

$a = \frac{2 F R^{2}}{I} \Rightarrow \frac{a_{A}}{a_{B}} = \frac{I_{B}}{I_{A}}$

$Solid sphere (A) : I_{A} = \frac{2}{5} (5 m) R^{2} + (5 m) R^{2} = 7 m R^{2}$

$Spherical shell (B) : I_{B} = \frac{2}{3} m R^{2} + m R^{2} = \frac{5}{3} m R^{2}$

$\frac{a_{A}}{a_{B}} = \frac{I_{B}}{I_{A}} = \frac{\frac{5}{3} m R^{2}}{7 m R^{2}} = \frac{5}{21}$

Solution

1 5 : 21

2 6 : 10

3 21 : 25

4 1 : 5

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