An inclined plane making an angle of $$300$$ with the horizontal is placed in a uniform horizontal electric field of $$100$$ Vm . A particle of mass $$1kg$$ and charge $$0.01C$$ is allowed to slide down from rest from height of $$1m$$. If the coefficient of friction is $$0.2$$ , find the time taken by the particle to reach the bottom $$($$ in seconds $$)$$ . Take $$g=9.8$$ $$m/s2$$

Question

An inclined plane making an angle of $$300$$ with the horizontal is placed in a uniform horizontal electric field of $$100$$ Vm . A particle of mass $$1kg$$ and charge $$0.01C$$ is allowed to slide down from rest from height of $$1m$$. If the coefficient of friction is $$0.2$$ ,  find the time taken by the particle to reach the bottom $$($$ in seconds $$)$$ . Take  $$g=9.8$$ $$m/s2$$

Infinity Learn · Accepted Answer

electrostatic force, $$F=Eq$$ $$N=Eq$$ $$sin30o+mg$$ $$cos300$$  $$=$$ $$8.99N$$  Acceleration down the plane  $$a=mg$$ $$sin300$$−μN−Eq $$cos300m$$ ⇒a $$=$$ (1)(9.8) (12) $$-$$ (0.2)(8.99) $$-$$ (100)(0.01)(32) $$1$$ ⇒$$a=2.236$$ $$m/s2$$  Displacement along the plane $$S=1sin300=2m$$  Using $$s=ut+12at2$$ ⇒$$2=122.236t2$$ ⇒$$42.236=t2$$ ⇒$$t=1.34$$ $$sec$$

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