Exam

JEE Main

Year

2018

Date

15 April

Shift

Evening Shift

Mode

Online

Subject

Physics

Chapter

Laws of Motion

JEE Main 2018 · 15 April · Evening Shift · Online · Physics · Laws of Motion

A body of mass 2 ~kg slides down with an acceleration of 3 ~m / s^2...

A body of mass $2 \mathrm{~kg}$ slides down with an acceleration of $3 \mathrm{~m} / \mathrm{s}^2$ 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: $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$

Step-by-step solution

Equation of motion when the mass slides down $$\begin{aligned}&M g \sin \theta-f=M a \\ &\Rightarrow 10-f=6 \\ &\quad \left(M=2 \mathrm{~kg},a=3 \mathrm{~m}/ \mathrm{s}^2, \theta=30^{{}^{\circ}} \text{ given }\right)\\ &\therefore f=4 \mathrm{~N} \end{aligned}$${ Equation\text{ of }\text{ motion }\text{ when }\text{ the }\text{ block }\text{ is } }$pushed up Let the external force required to take the block up the plane with same acceleration be$F $$\begin{aligned}&F-M g \sin \theta-f=M a \\ &\Rightarrow F-10-4=6 \\ &F=20 \mathrm{~N} \end{aligned}$$$