An inclined plane making an angle of 30^{circ} with horizontal is placed in a uniform horizontal ele

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1. Electric Charges and Fields

hard

An inclined plane making an angle of $30^{\circ}$ with the horizontal is placed in a uniform horizontal electric field $200 \, \frac{ N }{ C }$ as shown in the figure. A body of mass $1\, kg$ and charge $5\, mC$ is allowed to slide down from rest at a height of $1\, m$. If the coefficient of friction is $0.2,$ find the time (in $s$ )taken by the body to reach the bottom. $\left[ g =9.8 \,m / s ^{2}, \sin 30^{\circ}=\frac{1}{2}\right.$; $\left.\cos 30^{\circ}=\frac{\sqrt{3}}{2}\right]$

A

$0.92$

B

$0.46$

C

$2.3$

D

$1.3$

(JEE MAIN-2021)

Solution

$FBD$

here $N =9.8 \cos 30+1 \sin 30$

$\approx 9 \,N$

so $a=\frac{9.8 \sin 30-1 \cos 30-\mu \,N}{1}$

$a=2.233\, m / s ^{2}$

By $S=u t+\frac{1}{2} a t^{2}$

$=\frac{1}{2}(2.233) t ^{2}$

$\sin 30^{\circ}$

$t \approx 1.3\, sec$

Standard 12

Physics

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