A ball of mass 10 kg, moving with a velocity \(10 \sqrt{3} \mathrm{~m} / \mathrm{s}\) along the x-axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while second ball disintegrates into two equal pieces. One piece starts moving along y-axis with a speed of \(10 \mathrm{~m} / \mathrm{s}\). The second piece starts moving at an angle of \(30^{0}\) with respect to the x-axis. The velocity of the ball moving at \(30^{0}\) with \(x\)-axis is \(x \mathrm{~m} / \mathrm{s}\). The configuration of pieces after collision is shown in the figure below. The value of \(x\) to the nearest integer is ______

JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Conservation of Momentum

A ball of mass 10 kg, moving with a velocity

103 m / s

along the x-axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while second ball disintegrates into two equal pieces. One piece starts moving along y-axis with a speed of

10 m / s

. The second piece starts moving at an angle of

3 0^{0}

with respect to the x-axis.
The velocity of the ball moving at

3 0^{0}

with

x

-axis is

x m / s

.
The configuration of pieces after collision is shown in the figure below.
The value of

x

to the nearest integer is ______

Answer: 20

Solution

The first ball comes to rest, so after the collision the entire momentum is carried by the two

10

kg pieces. The initial momentum lies along the

x

-axis, so the

y

-components of the two pieces must cancel. One piece moves up the

y

-axis at

10

m/s and the other moves at

3 0^{\circ}

below the

x

-axis with speed

v

10 \times 10 - 10 v sin 3 0^{\circ} = 0 \Rightarrow v = 20 m/s

The

x

-equation agrees with this, since

10 v cos 3 0^{\circ} = 10 \times 20 \times \frac{3}{2} = 1003

equals the initial

10 \times 103

. The speed of the piece moving at

3 0^{\circ}

with the

x

-axis is

20

m/s.

JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Integer answer

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JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Conservation of Momentum

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