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  4. An inclined plane making an angle of 30° with the horizontal is placed in a uniform horizontal electric field 200 ( 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 taken by the body to reach the bottom. [ g =9.8 m / s 2, sin 30°=(1/2).; . cos 30°=(√3/2)] <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/9982f8e517273a97ddbe7197ed245360-.png />

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Q. 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 taken by the body to reach the bottom. $\left[ g =9.8 m / s ^{2}, \sin 30^{\circ}=\frac{1}{2}\right.$; $\left.\cos 30^{\circ}=\frac{\sqrt{3}}{2}\right]$
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JEE MainJEE Main 2021Laws of Motion

Solution:

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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 $S = ut +\frac{1}{2} at ^{2}$
$=\frac{1}{2}(2.233) t ^{2}$
$\sin 30^{\circ}$
$t \approx 1.3 sec$