A simple pendulum of bob of mass m and length l has one of its ends fixed at the centre O of a vertical circle- as shown in the figure- If -60- at the point P- the minimum speed u that should be given to the bob so that it completes a vertical circle isB- -2 gl C- -5 gl -2D -3 g l -2

The correct option is B √(2gl) At point B, T_B + mg = mv_B^2l For particle to complete vertical circle, T_B≥ 0 ⇒mv_B^2L≥ mg ⇒ nbsp; v_B^2≥ gL — (1) Applying ...

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Standard XII

Physics

Centripetal Acceleration

A simple pend...

Question

A simple pendulum of bob of mass $m$ and length $l$ has one of its ends fixed at the centre $O$ of a vertical circle, as shown in the figure. If $θ = 60^{\circ}$ at the point P, the minimum speed $u$ that should be given to the bob so that it completes a vertical circle is

\sqrt{g l}

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\sqrt{2 g l}

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\sqrt{\frac{5 g l}{2}}

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\sqrt{\frac{3 g l}{2}}

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Solution

The correct option is B $\sqrt{2 g l}$

At point B,
$T_{B} + m g = \frac{m v_{B}^{2}}{l}$
For particle to complete vertical circle,
$T_{B} \geq 0$
$\Rightarrow \frac{m v_{B}^{2}}{L} \geq m g$
$\Rightarrow v_{B}^{2} \geq g L$ --- (1)

Applying conservation of energy principle,
$\frac{1}{2} m v_{A}^{2} = m g l (1 - cos θ) + \frac{1}{2} m v_{B}^{2}$
$\frac{1}{2} m v_{A}^{2} = m g l (1 - \frac{1}{2}) + \frac{1}{2} m g l$
$\Rightarrow v_{A} = \sqrt{2 g l}$ is the minimum speed that must be given to the bob.

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A simple pendulum of bob of mass m and length l has one of its ends fixed at the centre O of a vertical circle, as shown in the figure. If θ=60∘ at the point P, the minimum speed u that should be given to the bob so that it completes a vertical circle is

The correct option is B √2gl At point B, TB+mg=mv2Bl For particle to complete vertical circle, TB≥0 ⇒mv2BL≥mg ⇒v2B≥gL --- (1) Applying conservation of energy principle, 12mv2A=mgl(1−cosθ)+12mv2B 12mv2A=mgl(1−12)+12mgl ⇒vA=√2gl is the minimum speed that must be given to the bob.

A simple pendulum of bob of mass $m$ and length $l$ has one of its ends fixed at the centre $O$ of a vertical circle, as shown in the figure. If $θ = 60^{\circ}$ at the point P, the minimum speed $u$ that should be given to the bob so that it completes a vertical circle is