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Standard XII

Physics

General Gravity Problem

A ball is sus...

Question

A ball is suspended from the top of a cart by a light string of length $1.0$ m. The cart and the ball are initially moving to the right at constant speed V, as shown in figure (1). The cart comes to rest after colliding and sticking to a fixed bumper, as in figure (2). The suspended ball swings through a maximum angle $60^{\circ}$ . The initial speed V is (neglect friction and take $g = 10 m / s^{2}$ )

\sqrt{10} m / s

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2 \sqrt{5} m / s

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5 \sqrt{2} m / s

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4 m / s

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Solution

The correct option is A $\sqrt{10} m / s$
As the car comes to rest, the bumper is fixed and string does no work on the ball, energy conservation can be applied.
$\frac{1}{2} m V^{2} = m g (L - L c o s θ) \Rightarrow V = \sqrt{2 g L (1 - c o s θ)}$
On putting values, $V = \sqrt{10} m / s$

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The correct option is A √10 m/sAs the car comes to rest, the bumper is fixed and string does no work on the ball, energy conservation can be applied. 12mV2=mg(L−L cos θ)⇒V=√2gL(1−cos θ) On putting values, V=√10 m/s

The correct option is A $\sqrt{10} m / s$
As the car comes to rest, the bumper is fixed and string does no work on the ball, energy conservation can be applied.
$\frac{1}{2} m V^{2} = m g (L - L c o s θ) \Rightarrow V = \sqrt{2 g L (1 - c o s θ)}$
On putting values, $V = \sqrt{10} m / s$