An inclined plane makes an angle 30° with the horizontal. A groove OA =5 m cut in the plane makes an angle 30° with OX. A short smooth cylinder is free to slide down the influence of gravity. The time taken by the cylinder to reach from A to O is ( g =10 m / s 2)

Question

An inclined plane makes an angle 30° with the horizontal. A groove OA =5 m cut in the plane makes an angle 30° with OX. A short smooth cylinder is free to slide down the influence of gravity. The time taken by the cylinder to reach from A to O is ( g =10 m / s 2) (A) 4 s (B) 2 s (C) 2 √2 s (D) 1 s

Tardigrade Admin · Accepted Answer

Acceleration of smooth cylinder = (m g sin 2 30°/m)=g sin 2 30°=(g/4)=(10/4) s=5=(1/2) × (10/4) × t2 ⇒ t=√(10 × 4/10)=2 sec

Q. An inclined plane makes an angle $3 0^{\circ}$ with the horizontal. A groove OA $= 5 m$ cut in the plane makes an angle $3 0^{\circ}$ with OX. A short smooth cylinder is free to slide down the influence of gravity. The time taken by the cylinder to reach from $A$ to $O$ is $(g = 10 m / s^{2})$

$4 s$

$2 s$

$22$ s

$1 s$

Acceleration of smooth cylinder =
$\frac{m g s i n ^{2} 3 0 ^{\circ}}{m} = g sin^{2} 3 0^{\circ} = \frac{g}{4} = \frac{10}{4}$
$s = 5 = \frac{1}{2} \times \frac{10}{4} \times t^{2}$
$\Rightarrow t = \frac{10 \times 4}{10} = 2 sec$

Q. An inclined plane makes an angle 30∘ with the horizontal. A groove OA =5m cut in the plane makes an angle 30∘ with OX. A short smooth cylinder is free to slide down the influence of gravity. The time taken by the cylinder to reach from A to O is (g=10m/s2)

4s

2s

22​ s

1s