Question 395: Electrostatics & Capacitance

Question

An inclined plane making an angle of 30$^\circ$ with the horizontal is placed in a uniform horizontal electric field $200{N \over C}$ 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 taken by the body to reach the bottom.
[g = 9.8 m/s
2
; $\sin 30^\circ  = {1 \over 2}$; $\cos 30^\circ  = {{\sqrt 3 } \over 2}$]
![](https://imagex.cdn.examgoal.net/1kluw72wh/7b7d6f6e-b1e8-48d6-b2a5-146dc8eda7ce/cbcb9e10-7ceb-11eb-8f7b-79760a5d8011/file-1kluw72wi-284w.jpg)

Accepted Answer

f = mg sin$	heta$ $-$ ($\mu$N + qE cos$	heta$)
F = mg sin$	heta$ $-$ $\mu$(mg cos$	heta$ + qE sin$	heta$) $-$ qE cos$	heta$
F = 1 $	imes$ 10 $	imes$ sin30
$-$ 0.2 (1 $	imes$ 10 $	imes$ cos30$^\circ$ + 200 $	imes$ 5 $	imes$ 10
$-$3
sin30$^\circ$)
$-$ 200 $	imes$ 5 $	imes$ 10
$-$3
cos30$^\circ$
$ \Rightarrow $ F = 2.3 N
$a = {F \over m} = {{2.3} \over 1} = 2.3$ m/sec
2
$t = \sqrt {{{25} \over 9}}  = \sqrt {{{2 	imes 2} \over {2.3}}}  = 1.3$ sec
![](https://imagex.cdn.examgoal.net/1klwh3det/a60040dd-5de5-4a73-9c2a-ebfe9c5f38a6/4d0a0460-7dca-11eb-8899-2d60151feb7a/file-1klwh3deu-366w.png)

Answer

0.46 s

Answer

0.92 s

Answer

1.3 s

Answer

2.3 s

Electrostatics & Capacitance

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