An inclined plane making an angle of $$300$$ with the horizontal is placed in a uniform horizontal electric field $$200$$ $$N/C$$ as shown in the figure. A body of mass $$1kg$$ and charge $$5mC$$ is allowed to slide down from rest at a height of $$1$$ m. If the coefficient of friction is $$0.2$$ . Find the time taken by the body to reach the bottom. $$g=9.8m/s2$$; $$sin30o=12$$;$$cos30o=32$$

Question

An inclined plane making an angle of $$300$$ with the horizontal is placed in a uniform horizontal electric field $$200$$ $$N/C$$ as shown in the figure. A body of mass $$1kg$$ and charge $$5mC$$ is allowed to slide down from rest at a height of $$1$$ m. If the coefficient of friction is $$0.2$$ . Find the time taken by the body to reach the bottom. $$g=9.8m/s2$$; $$sin30o=12$$;$$cos30o=32$$

Infinity Learn · Accepted Answer

Perpendicular to plane, $$N=mgcos$$⁡θ$$+qEsin$$⁡θ Parallel to plane, $$a=mgsin$$⁡θ−[qEcos⁡θ$$+$$μN]m⇒$$ma=mgsin$$⁡θ−[qEcos⁡θ$$+$$μ(mgcos$$⁡θ$$+qEsin$$⁡θ$$)]⇒$$a=gsin$$⁡θ−qEcos⁡θ$$m+$$μgcos⁡θ$$+qEsin$$⁡θm⇒$$a=9.8$$×$$12$$−$$5$$×$$10$$−$$3$$×$$200$$×$$321+0.29.8$$×$$32+5$$×$$10$$−$$3$$×$$200$$×$$12$$⇒$$a=4.9$$−$$32$$−$$0.983$$−$$0.1=2.23ms$$−$$2$$ Now length of incline $$=hsin$$⁡$$300=11/2=2m$$ Equation of Kinematics, $$S=ut+12at2$$⇒$$2=0+12(2.23)t2$$⇒$$t=42.23=1.34s$$

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