JEE MAIN - Physics (2018 - 15th April Evening Slot - No. 23)
A body of mass 2 kg slides down with an acceleration of 3 m/s2 on a rough inclined plane having a slope of $${30^o}$$. The external force required to take the same body up the plane with the same acceleration will be : (g = 10 m/s2)
14 N
20 N
6 N
4 N
Explanation
When mass slide down then,
Mgsin$$\theta $$ $$-$$ $$\mu $$Mg cos$$\theta $$ = Ma
$$ \Rightarrow $$ $$\,\,\,$$ a = g(sin30o $$-$$ $$\mu $$ cos30o)
When mass pushed upward with force F,
F $$-$$ Mgsin$$\theta $$ $$-$$ $$\mu $$ Mgcos$$\theta $$ = Ma
$$ \Rightarrow $$ $$\,\,\,$$ F = Mg(sin30o + $$\mu $$ cos 30o) + Mg(sin30o $$-$$ $$\mu $$ cos30o)
$$ \Rightarrow $$ $$\,\,\,$$ F = 2Mg sin30o
= 2 $$ \times $$ 2 $$ \times $$ 10 $$ \times $$ $${1 \over 2}$$
= 20 N
Mgsin$$\theta $$ $$-$$ $$\mu $$Mg cos$$\theta $$ = Ma
$$ \Rightarrow $$ $$\,\,\,$$ a = g(sin30o $$-$$ $$\mu $$ cos30o)
When mass pushed upward with force F,
F $$-$$ Mgsin$$\theta $$ $$-$$ $$\mu $$ Mgcos$$\theta $$ = Ma
$$ \Rightarrow $$ $$\,\,\,$$ F = Mg(sin30o + $$\mu $$ cos 30o) + Mg(sin30o $$-$$ $$\mu $$ cos30o)
$$ \Rightarrow $$ $$\,\,\,$$ F = 2Mg sin30o
= 2 $$ \times $$ 2 $$ \times $$ 10 $$ \times $$ $${1 \over 2}$$
= 20 N
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