The block of mass $m_{2} = 10 k g$ is given a sharp impulse so that it acquires a velocity $v_{0} = 30 m / s$ towards right. Find the velocity of the centre of mass.( $m_{2} = 5 k g$ and $k = 30 N / m$ )

5 m / s

No worries! We‘ve got your back. Try BYJU‘S free classes today!

10 m / s

No worries! We‘ve got your back. Try BYJU‘S free classes today!

15 m / s

No worries! We‘ve got your back. Try BYJU‘S free classes today!

20 m / s

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $20 m / s$
Mass of block 1 & 2, $m_{1} = 10 k g a n d m_{2} = 5 k g$
Initial velocity 1 & 2, $v_{1} = 30 m s^{- 1} a n d v_{2} = 0$
From conservation of momentum
Initial momentum = momentum of center of mass
$m_{1} u_{1} + m_{2} u_{2} = (m_{1} + m_{2}) V_{c m}$
$\Rightarrow V_{c m} = \frac{m_{1} u_{1} + m_{2} u_{2}}{m_{1} + m_{2}} = \frac{10 \times 30 + 5 \times 0}{10 + 0} = 20 m s^{- 1}$
Hence, center of mass velocity is $20 m s^{- 1}$

Suggest Corrections

Similar questions

Q. Two blocks of masses m₁ and m₂ are connected by a spring of spring constant k. The block of mass m₂ is given a sharp impulse so that it acquires a velocity v₀ towards right. Find (a) the velocity of the centre of mass, (b) the maximum elongation that the spring will suffer.
Figure

Q. Two blocks of masses

m_{1}

and

m_{2}

are connected by a spring of spring constant

k

. The block of mass

m_{2}

is given a sharp impulse so that it acquires a velocity

v_{0}

towards right. Find the maximum elongation that the spring will suffer.

Two blocks of masses $m_{1}$ and $m_{2}$ are connected by a spring of constant k (given figure).The block of mass $m_{2}$ is given a sharp impulse so that it acquires a velocity $v_{0}$ towards right.Find (a) the velocity of the centre of mass,(b) the maximum elongation that the spring will suffer.