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.

Question

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.

Infinity Learn · Accepted Answer

$$R=mgcos30$$°$$+qEsin30$$°$$=1032+0.01$$×$$1002=53+0.5=9.16$$ N Frictional force $$Fs=$$μ$$R=0.2$$×$$9.16=1.832$$ 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 $$=1$$×$$cosec30$$°$$=2$$ $$ms=ut+(1/2)ft2$$,$$u=0$$∴$$t=(2$$ $$sf)1/2=(2$$×$$22.3)1/2=1.32sec$$

Electric field

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