JEE Main 2026 · 6 Apr · Shift 2 · Physics Q28

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PhysicsSingle correct+4 / -1Question 28 of 75

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 ________.

5 : 21

6 : 10

21 : 25

1 : 5

Answer and worked solution

Official answer: A

Force at the top, rolling. With friction f forward and $k=\dfrac I{MR^2}$ :
$F+f=Ma,\qquad (F-f)R=I\frac aR\ \Rightarrow\ a=\frac{2F}{M(1+k)}.$

Each body.

Solid sphere ( $5m$ , $k=\tfrac25$ ): $a_A=\dfrac{2F}{7m}$ .
Shell ( $m$ , $k=\tfrac23$ ): $a_B=\dfrac{6F}{5m}$ .

Ratio: $\dfrac{2/7}{6/5}=\dfrac5{21}$ .

(A)

Topics:Rolling motion Moment of inertia

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JEE Main 2026 · 6 Apr · Shift 2, Physics question 28