Question

-Force F is double the minimum force required
to keep the block moving with constant speed
on a smooth incline. Acceleration of the block​

Answer 1

$\Large\boxed{\sf{\quad(2)\quad\!g\sin\theta\quad}}$

Free body diagram of the block on smooth inclined plane is shown in the fig., from which we get that the force due to which the block slides down the plane is $\sf{mg\sin\theta.}$

Hence the minimum force required to keep the block moving with constant speed (or without acceleration) over the plane is $\sf{mg\sin\theta}$ also, but upwards along the plane.

By the question, we have,

$\longrightarrow\sf{F=2mg\sin\theta}$

Let $\sf{a}$ be the net acceleration acting on the block upwards along the plane, due to the applied force $\sf{F.}$ Then,

$\longrightarrow\sf{F-mg\sin\theta=ma}$

$\longrightarrow\sf{2mg\sin\theta-mg\sin\theta=ma}$

$\longrightarrow\sf{mg\sin\theta=ma}$

$\longrightarrow\sf{\underline{\underline{a=g\sin\theta}}}$