Question

A $1kg$ solid sphere rolls without slipping on a rough horizontal surface under the influence of a $7N$ force. The force acts tangentially at the highest point of the sphere. Which of the following statements are correct? ($7N$ force acts towards right ).

• A. The frictional force on the sphere acts towards right.
• B. The value of the frictional force is $3N$.
• C. The acceleration of the centre of the sphere is $9.8m/s^2$.
• D. The acceleration of the centre of the sphere is $10m/s^2$.

Answer 1

Answer: (A), (B), (D)

The correct options are
A The frictional force on the sphere acts towards right.
B The value of the frictional force is $3N$.
D The acceleration of the centre of the sphere is $10m/s^2$.

Given: $m=1kg$

Let the friction force acts towards right.

$(F-f)R=I\alpha$

$(7-f)R=\frac{2}{5}m{R}^2\alpha$

$⟹7-f=\frac{2}{5}a$ as $(a=R\alpha )$

Also, $ma=F+f⟹a=7+f$

Solving gives $f=+3N$ (+ sign indicates that our assumption is correct)

Thus $a=7+3=10m/s^2$