JEE Mains · Physics · STD 11 - Work,energy,power and collision
- JEE Mains 2021
- Hard
- Numerical
A ball of mass \(10\, kg\) moving with a velocity \(10 \sqrt{3} m / s\) along the \(x-\)axis, hits another ball of mass \(20\, kg\) which is at rest. After the collision, first ball comes to rest while the 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 \(30^{\circ}\) with respect to the \(x-\)axis. The velocity of the ball moving at \(30^{\circ}\) 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
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Answer & Solution
Correct Answer
(C) \(20\)
Step-by-step Solution
Detailed explanation
Let velocity of \(2^{\text {nd }}\) fragment is \(\vec{v}\) then by conservation of linear momentum
\(10(10 \sqrt{3}) \hat{ i }=(10)(10 \hat{ j })+10 \overrightarrow{ v }\)
\(\Rightarrow \overrightarrow{ v }=10 \sqrt{3} \hat{ i }-10 \hat{ j }\)
\(|\overrightarrow{ v }|=\sqrt{300+100}=\sqrt{400}=20 m / s\)
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