JEE Main · 2022 · 27 Jul 2022 · Shift 2 · Kinematics

A block 'A' takes 2 s to slide down a frictionless incline of

3 0^{\circ}

and length '

l

', kept inside a lift going up with uniform velocity '

v

'. If the incline is changed to

4 5^{\circ}

, the time taken by the block, to slide down the incline, will be approximately:

(A)2.66 s
(B)0.83 s
(C)1.68 s✓ Correct
(D)0.70 s

Answer: (C)

Solution

Since the lift moves with uniform velocity, the effective acceleration is just

a = g sin θ

. For

3 0^{\circ}

ℓ = \frac{1}{2} g sin 3 0^{\circ} \times 2^{2} = g

. For

4 5^{\circ}

ℓ = \frac{1}{2} g sin 4 5^{\circ} \times t^{2}

. Substituting

ℓ = g

g = \frac{1}{2} g \times \frac{1}{2} \times t^{2}

, giving

t^{2} = 22

, so

t = 22 \approx 1.68

JEE Main · 2022 · 27 Jul 2022 · Shift 2 · Single correct option

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