Question

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

• A. 14 N
• B. 20 N
• C. 6 N
• D. 4 N

Answer 1

Answer: (B)

Equation of motion when the mass slides down is
$m g \sin \theta-f=m a$

Given: $m=2\, kg ; \sin 30^{\circ}=\frac{1}{2} ;\, g=10 \,m / s ; a=3 \,m / s ^{2}$
Therefore, from Eq. (1), we have $f=m g \,\sin \,\theta-ma=2 \times 10 \times \frac{1}{2}-2 \times 3=4 \,N$
Equation of motion when mass is pushed upward is $F-m g \sin \theta-f=m a$
$F=m g \,\sin \,\theta+m a+f=2 \times 10 \times \frac{1}{2}+2 \times 3+4$
$F=10+6+4=20\, N$