(D) First,calculate the time taken by both objects to reach the ground from height $h = 20\,m$ using $h = \frac{1}{2}gt^2$:$t = \sqrt{\frac{2h}{g}} =

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(D) First,calculate the time taken by both objects to reach the ground from height $h = 20\,m$ using $h = \frac{1}{2}gt^2$:$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 20}{10}} = \sqrt{4} = 2\,s$.Let $v_1$ be the velocity of the ball and $v_2$ be the velocity of the bullet after the collision.For the ball: $v_1 = \frac{\text{distance}}{\text{time}} = \frac{30}{2} = 15\,m/s$.For the bullet: $v_2 = \frac{\text{distance}}{\text{time}} = \frac{120}{2} = 60\,m/s$.Using the law of conservation of linear momentum in the horizontal direction:$m_{bullet} u = m_{ball} v_1 + m_{bullet} v_2$$(0.01) u = (0.2)(15) + (0.01)(60)$$0.01 u = 3 + 0.6 = 3.6$$u = \frac{3.6}{0.01} = 360\,m/s$.

Class 11 Physics Laws of Motion Conservation of Linear Momentum

Difficult

$A$ ball of mass $200\,g$ rests on a vertical post of height $20\,m$. $A$ bullet of mass $10\,g$,travelling in a horizontal direction,hits the centre of the ball. After the collision,both travel independently. The ball hits the ground at a distance of $30\,m$ and the bullet at a distance of $120\,m$ from the foot of the post. The value of the initial velocity of the bullet will be $............m/s$ (if $g = 10\,m/s^2$).

JEE MAIN 2023 All JEE MAIN

A
$120$
B
$60$
C
$400$
D
$360$

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EasyWBJEE 2013

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DifficultTS EAMCET 2010

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$A$ stationary body of mass $m$ explodes into $3$ parts having masses in the ratio $1 : 3 : 3$. The two parts having equal mass move at right angles to each other with a velocity of $15\,m/s$. What is the velocity of the third part?

Medium

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Neglecting friction,if a person sitting at the back of a motorcycle moving on a straight path falls off while the motorcycle is in motion,will the velocity of the motorcycle increase or decrease? Why?

Easy

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An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $1 \, kg$ moves with a speed of $12 \, m s^{-1}$ and the second part of mass $2 \, kg$ moves with $8 \, m s^{-1}$ speed. If the third part flies off with $4 \, m s^{-1}$ speed,then its mass is ......... $kg$.

MediumAIPMT 2009

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$A$ shell of mass $5 M$, acted upon by no external force and initially at rest, bursts into three fragments of masses $M, 2 M$, and $2 M$ respectively. The first two fragments move in opposite directions with velocities of magnitudes $2 v$ and $v$ respectively. The third fragment will

$A$ stationary body of mass $m$ explodes into $3$ parts having masses in the ratio $1 : 3 : 3$. The two parts having equal mass move at right angles to each other with a velocity of $15\,m/s$. What is the velocity of the third part?

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