A block starts moving up an inclined plane of inclination 30° with an initial velocity of v0. It comes back to its initial position with velocity (v0/2) . The value of the coefficient of kinetic friction between the block and the inclined plane is close to (I /1000), The nearest integer to I is .

Question

A block starts moving up an inclined plane of inclination 30° with an initial velocity of v0. It comes back to its initial position with velocity (v0/2) . The value of the coefficient of kinetic friction between the block and the inclined plane is close to (I /1000), The nearest integer to I is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/3fee5e0b82f96902b93d12c8b03a44cd-.png" /> ∴ (1/2) v 0 ( v 0/ a 1)=(1/2)(( v 0/2))(( v 0/2 a 1)) ⇒ 3 sin θ=5 μ cos θ ∴ μ=√3 / 5

∴21​v0​a1​v0​​=21​(2v0​​)(2a1​v0​​) ⇒3sinθ=5μcosθ ∴μ=3​/5

$∴ \frac{1}{2} v_{0} \frac{v _{0}}{a _{1}} = \frac{1}{2} (\frac{v _{0}}{2}) (\frac{v _{0}}{2 a _{1}})$
$\Rightarrow 3 sin θ = 5 μ cos θ$
$∴ μ = 3 /5$