Question

A block is placed on top of a fixed smooth inclined plane inclined at 30° to horizontal. The length of plane is 5 m. The block slides down the plane and reaches at bottom. The speed of the block at bottom will be nearly

Answer 1

$\text{By the condition of the problem, }\newline \text{we have a smooth inclined plane.}$

$\text{That is, frictional forces can be neglected.}$

$l = 5m$

$h = l*\sin30\degree= 2.5m$

$E = E_p+E_k$

$\text{At the top of an inclined plane:}$

$E_p = mgh;E_k=0$

$\text{At the foot of an inclined plane:}$

$E = E_p'+E_k'$

$E_k'=\frac{mv^2}{2};E_p'=0;$

$mgh = \frac{mv^2}{2}$

$v=\sqrt{2gh}=\sqrt{2*9.8*2.5}=7\frac{m}{s}$

$\text{Answer: }v=7\frac{m}{s}$