Question

A disc of mass m and radius R is placed over plank of mass m. there is sufficient friction between disc & plank to prevent slipping. A force F is applied at centre of disc then.

• A. Acceleration of plank is $\frac{F}{2m}$
• B. Acceleration of plank is $\frac{F}{4m}$
• C. Friction force between disc and plank is $\frac{F}{7}$
• D. Friction force between disc and plank is $\frac{F}{3}$

Answer 1

The correct option is B Acceleration of plank is $\frac{F}{4m}$

$\begin{array}{c}\text{Correct option is (B)}\\ \text{Let the friction force be}f\text{and angular}\\ \text{acceleration be}\alpha \\ \text{Acceleration of disc through centre}=a_1\text{and}\\ \text{of plank is}{a}_2\\ \text{so,}\\ \text{Tork through contact point;}\tau =I\alpha \\ FR=\frac{m{B}^2\alpha --\left(i\right)}{2}\\ \begin{array}{cc}{a}_1-\alpha R=a_2& \\ a_1-\alpha R=\frac{f}{m}& \\ a_1=\frac{3R\alpha }{2};\frac{F}{m}=2\alpha R& \end{array}\\ \alpha =\frac{F}{2mR}\\ a_2=\frac{R\alpha }{2}=\frac{F}{4m}\end{array}$