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 $30^o$ . The external force required to take the same body up the plane with the same acceleration will be $... N$ $(g\, = 10\, m/s^2)$
JEE MAIN 2018, Difficult
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Equation of motion when the mass slides down
$M g \sin \theta-f=M a$
$\Rightarrow 10-f=6$
$\quad\left(M=2 k g, a=3 m / s^2, \theta=30^{\circ} \text { given }\right)$
$\therefore f=4 N$
Equation of motion when the block is
pushed up
Let the external
force required to
take the block up the
plan with same
acceleration be $F$
$F-M g \sin \theta-f=M a$
$\Rightarrow F-10-4=6$
$F=20 N$
$M g \sin \theta-f=M a$
$\Rightarrow 10-f=6$
$\quad\left(M=2 k g, a=3 m / s^2, \theta=30^{\circ} \text { given }\right)$
$\therefore f=4 N$
Equation of motion when the block is
pushed up
Let the external
force required to
take the block up the
plan with same
acceleration be $F$
$F-M g \sin \theta-f=M a$
$\Rightarrow F-10-4=6$
$F=20 N$
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