# A block starts moving up an inclined plane of inclination $30^{\circ}$ with an initial velocity of $\nu _{0}$. It comes back to its initial position with velocity $\frac{\nu _{0}}{2}.$ The value of the coefficient of kinetic friction between the block and the inclined plane is close to $\frac{I}{1000},$ The nearest integer to $I$ is _______. Option: 1 346 Option: 2 12345 Option: 3 7689 Option: 4 12341

Let the length of the inclined plane as S (as shown in the figure)

For upward motion

\begin{aligned} &\text { from work energy theorem }\\ &W_{f}=k_{f}-k_{i} \end{aligned}

So

$\frac{1}{2} m v_{0}^{2}=\left(m g \frac{S}{2}+\mu m g \frac{\sqrt{3}}{2} S\right)....(1)$

For downward motion

\begin{aligned} &\text { from work energy theorem }\\ &W_{f}=k_{f}-k_{i} \end{aligned}

$\frac{1}{2} \frac{m v_{0}^{2}}{4}=\left(m g \frac{S}{2}-\mu m g \frac{\sqrt{3}}{2} \cdot S\right).......(2)$

From equation (1) and (2)

we get

$\begin{array}{l} 4=\frac{(1+\mu \sqrt{3})}{(1-\mu \sqrt{3})} \\ \\ \Rightarrow 4-4 \mu \sqrt{3}=1+\mu \sqrt{3} \\ \Rightarrow 3=5 \mu \sqrt{3} \\ \\ \therefore \mu=\frac{\sqrt{3}}{5} \approx \frac{346.41}{1000} \\ I=346 \end{array}$

## Most Viewed Questions

### Preparation Products

##### Knockout JEE Main 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
##### Knockout JEE Main 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
##### Test Series JEE Main 2021

Chapter/Subject/Full Mock Tests for JEE Main, Personalized Performance Report, Weakness Sheet, Complete Answer Key,.

₹ 6999/- ₹ 2999/-
##### Knockout JEE Main 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Live Classes(Classes will start from Last week of September), Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 24999/-