Question

A body mass of $2kg$ slides down with an acceleration of $3m{s}^{-2}$ on a rough inclined plane having a slope of ${30}^o$. The external force required to take the same acceleration will be : $(g=10m{s}^{-2})$

• A. $14N$
• B. $20N$
• C. $6N$
• D. $4N$

Answer 1

The correct option is B $20N$

Friction force acting up the inclined plane due to sliding

shown in the diagram 1

Let f is the friction force ,a is an acceleration

$mgcos\theta -f=ma$

$\Rightarrow 20sin{30}^0-f=2\times 3$

$\Rightarrow f=(10-6)=4N$

Let external force F is acting up to inclined plane shown in diagram 2.

$F-mgsin\theta -f=ma$ $(f=4N)$

$\Rightarrow F=2\times 3+20sin{30}^0+4=6+10+4=20N$

Hence B option is correct.