Question

A block ‘A’ takes 2 s to slide down a frictionless incline of 30° and length ‘l’, kept inside a lift going up with uniform velocity ‘v’. If the incline is changed to 45°, 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
• D. 0.70 s

Answer 1

The Correct Option is C

The correct answer is (C) : 1.68
\(θ_1 = 30°, θ_2 = 45°\)
\(a_1 = g\sinθ_1 = 5m/s^2, a_2 = g\sinθ_2\)
\(= 5\sqrt2m/s^2\)
\(\frac{t_1}{t_2} = \frac{\sqrt{\frac{2l}{a_1}}}{\sqrt{\frac{2l}{a_2}}} = \sqrt{\frac{a_2}{a_1}}\)
\(\frac{t_1}{t_2} = (2)^{\frac{1}{4}}\)
\(t_2 = (2)^{\frac{3}{4}}\)
≈ 1.68s