# Centre of mass

## A man weighing 80 kg is standing in a trolley weighing 320 kg . The trolley is resting on a frictionless horizontal rails . If the man starts walking on the trolley with speed of 1 m/s , then after 4 sec his displacement relative to the ground will be

Q: A man weighing 80 kg is standing in a trolley weighing 320 kg . The trolley is resting on a frictionless horizontal rails . If the man starts walking on the trolley with speed of 1 m/s , then after 4 sec his displacement relative to the ground will be

(a)5 m

(b) 4.8 m

(c) 3.2 m

(d) 3.0 m

Ans: (c)
Sol: On applying conservation of linear momentum ,

80 x 1 = (80 + 320)v

v = 0.2 m/s

Velocity of man with respect ot ground = 1.0 – 0.2 = 0.8 m/s

Displacement of man relative to the ground

= 0.8 × 4 = 3.2 m

## Two bodies of different masses of 2 kg and 4 kg are moving with velocities 20 m/s and 10 m/s towards each other due to mutual gravitational attraction. What is the velocity of their centre of mass

Q: Two bodies of different masses of 2 kg and 4 kg are moving with velocities 20 m/s and 10 m/s towards each other due to mutual gravitational attraction. What is the velocity of their centre of mass

(a) 5 m/s

(b) 6 m/s

(c) 8 m/s

(d) Zero

Ans: (d)

## Two object of masses 200 g and 500 g possess velocities 10i m/s and ( 3i + 5j ) m/s respectively. The velocity of their centre of mass in m/s is

Q: Two object of masses 200 g and 500 g possess velocities 10 i m/s and ( 3i + 5j ) m/s respectively. The velocity of their centre of mass in m/s is

(a) 5i – 25j

(b) 7/5 i – 25j

(c) 5i + 25/7 j

(d) 25i – 5/7 j

Ans: (c)
Sol: $\displaystyle \vec{v_{cm}} = \frac{m_1 \vec{v_1} + m_2 \vec{v_2}}{m_1 + m_2}$

$\displaystyle \vec{v_{cm}} = \frac{200 \times 10 \hat{i} + 500 \times (3 \hat{i}+ 5 \hat{j})}{200 + 500}$

$\displaystyle \vec{v_{cm}} = \frac{20 \hat{i} + 5 (3 \hat{i}+ 5 \hat{j})}{7}$

$\displaystyle \vec{v_{cm}} = \frac{35 \hat{i} + 25 \hat{j}}{7}$

$\displaystyle \vec{v_{cm}} = 5 \hat{i} + \frac{25}{7}\hat{j}$

## A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass….

Q: A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed of 2 m/s. When the stone reaches the floor, the distance of the man above the floor will be

(a) 20 m

(b) 9.9 m

(c) 10.1 m

(d) 10 m

Ans: (c)

## A 2 kg body and a 3 kg body are moving alone the x-axis. At a particular instant the 2 kg body has a velocity of 3 m/s and ….

Q: A 2 kg body and a 3 kg body are moving alone the x-axis. At a particular instant the 2 kg body has a velocity of 3 m/s and the 3 kg body has the velocity of 2 m/s. The velocity of the centre of mass at that instant is

(a) 5 m/s

(b) 1 m/s

(c) 0

(d) None of these