An inclined plane making an angle of 30° with the horizontal is placed in a uniform electric field of intensity 100 V/m. A particle of mass 1 kg and charge 0.01C is allowed to slide down from rest on the plane from a height of 1m. If the coefficient of friction is 0.2, then find the time taken (in second) by the particle to reach the bottom.

R=mgcos30°+qEsin30°=1032+0.01×1002=53+0.5=9.16 N Frictional force Fs=μR=0.2×9.16=1.832 N Resultant force along the plane in the downward direction F=mgsin30°−(Fs+qEcos30°)=5−(1.832+0.01×100×1.7322)=5−2.698=2.3 N∴ Acceleration along the plane, f=Fm=2.3 m/sec2 Distance along the plane =1×cosec30°=2 ms=ut+(1/2)ft2,u=0∴t=(2 sf)1/2=(2×22.3)1/2=1.32sec