Question

a block of metal mass 50 gram when placed over an inclined plane at an angle of 15 degrees slides down without acceleration if the inclination is increased by 15 degree what would be the acceleration of the block.

Answer 1

a block of mass 50g or 0.05g when over an inclined plane at an angle of 15° slides down without acceleration, means body is in uniform motion. means, a force acts just opposite to motion of body e.g., frictional force.
so, $mgsin15^{\circ}=\mu mgcos15^{\circ}$
$\mu=tan15^{\circ}=2-\sqrt{3}$

now, when inclination is increased by 15° then,
acceleration of body is given by
$a=g(sin30^{\circ}-\mu cos30^{\circ})$
a = 10 × [0.5 - (2 - √3) × √3/2]
= 10 × 0.2679
= 2.679 m/s²