Question

23
20. In the figure given below, a child of mass 4 kg is
standing on a wooden plank of mass 40 kg which
is kept at rest on a horizontal smooth ground.
If child walks on the plank with a velocity of
10 m/s with respect to plank, then the speed of
the plank w.r.t. ground will be [NCERT Pg. 148]
v = 10 m/s
Woch
TAL​

Answer 1

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Answer 2

Given:

A child of mass 4 kg ,

wooden plank of mass 40 kg

Explanation:

The Law of Conservation of Momentum is useful in describing the momentum of a system of objects. In its simplest terms, the Law of Conservation of Momentum tells us that the total momentum of an isolated system remains constant.

The formula for the Law of Conservation of Momentum is p=p' or m1v1+m2v2=m1v1'+m2v2'. This equation shows us that the sum of the momentum of all the objects in the system is constant.

$m_{1} v_{1} +m_{2} v_{2}=m_{1}u_{1}+m_{2}u_{2}$

here,

$m_{1} u_{1}=(m_{1}+m_{2} )v_{2}$

$v_{2}$ is the velocity of center of mass of system

$4*10=(4+40)v_{2}$

$40=(44)v_{2}$

44 is multiply value in right side change into divide value in left side

$v_{2}=\frac{40}{44}$

divide the values

$v_{2} =\frac{10}{11}$

∴ The answer is  $v_{2} =\frac{10}{11}$