Shown in the figure is a block at rest having an inclined smooth groove in a vertical plane. The horizontal surface is smooth. A ball of the same mass as that of the block at rest is released from the top end. The time when the ball will leave groove is √(n L/2 √3 g) . Find n .

Question

Shown in the figure is a block at rest having an inclined smooth groove in a vertical plane. The horizontal surface is smooth. A ball of the same mass as that of the block at rest is released from the top end. The time when the ball will leave groove is √(n L/2 √3 g) . Find n . <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-erfpqruiehlc.png" /> (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-erfpqrui1qev.png" /> -mv cos 60o + 2mu=0 ⇒ v=4u (1/2)m [.v2 +u2 +2uv cos 120° ].+(1/2)mu2 =mgx sin60° ⇒ v2=(8/7)√3 gx ⇒ ar = (4 √3/7)g ∴ t=√(2 L × 7/4 √3 g)

Q. Shown in the figure is a block at rest having an inclined smooth groove in a vertical plane. The horizontal surface is smooth. A ball of the same mass as that of the block at rest is released from the top end. The time when the ball will leave groove is $\frac{n L}{2 3 g}$ . Find $n$ .

$- m v cos 6 0^{o} + 2 m u = 0 \Rightarrow v = 4 u$
$\frac{1}{2} m [v^{2} + u^{2} + 2 uv cos 12 0^{\circ}] + \frac{1}{2} m u^{2} = m gx s in 6 0^{\circ}$
$\Rightarrow v^{2} = \frac{8}{7} 3 gx \Rightarrow a_{r} = \frac{4 3}{7} g$
$∴ t = \frac{2 L \times 7}{4 3 g}$

Q. Shown in the figure is a block at rest having an inclined smooth groove in a vertical plane. The horizontal surface is smooth. A ball of the same mass as that of the block at rest is released from the top end. The time when the ball will leave groove is 23​gnL​​ . Find n .

−mvcos60o+2mu=0⇒v=4u 21​m[v2+u2+2uvcos120∘]+21​mu2=mgxsin60∘ ⇒v2=78​3​gx⇒ar​=743​​g ∴t=43​g2L×7​​

Q. Shown in the figure is a block at rest having an inclined smooth groove in a vertical plane. The horizontal surface is smooth. A ball of the same mass as that of the block at rest is released from the top end. The time when the ball will leave groove is $\frac{n L}{2 3 g}$ . Find $n$ .

$- m v cos 6 0^{o} + 2 m u = 0 \Rightarrow v = 4 u$
$\frac{1}{2} m [v^{2} + u^{2} + 2 uv cos 12 0^{\circ}] + \frac{1}{2} m u^{2} = m gx s in 6 0^{\circ}$
$\Rightarrow v^{2} = \frac{8}{7} 3 gx \Rightarrow a_{r} = \frac{4 3}{7} g$
$∴ t = \frac{2 L \times 7}{4 3 g}$