A tangential force F acts at the top of a thin spherical shell of mass m and radius R . The acceleration of the shell, if it rolls without slipping is

Question

A tangential force F acts at the top of a thin spherical shell of mass m and radius R . The acceleration of the shell, if it rolls without slipping is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-jtq4j2r5p1bn63a6.jpg" /> (A) (5 F/6 m) (B) (6 F/5 m) (C) (7 m/2 F) (D) (2 m/7 F)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-jtq4j2r5p1bnlopk.jpg" /> torque about 'O' τ = I α F (. 2 R .) = α (5/3) m R2 α = (6 F/5 m R) Linear acceleration a = R α = (6 F/5 m)

Q. A tangential force $F$ acts at the top of a thin spherical shell of mass $m$ and radius $R$ . The acceleration of the shell, if it rolls without slipping is

$\frac{5 F}{6 m}$

$\frac{6 F}{5 m}$

$\frac{7 m}{2 F}$

$\frac{2 m}{7 F}$

torque about 'O' $τ = I α$
$F (2 R) = α \frac{5}{3} m R^{2}$
$α = \frac{6 F}{5 m R}$
Linear acceleration $a = R α = \frac{6 F}{5 m}$

Q. A tangential force F acts at the top of a thin spherical shell of mass m and radius R . The acceleration of the shell, if it rolls without slipping is

6m5F​

5m6F​

2F7m​

7F2m​