Question

A trolley of mass m is moving over a smooth surface with velocity v. If a body of certain mass is gently placed on it, its velocity decreases by 20%. The mass of the body placed over the trolley is

Answer 1

Solution :

Mass of the body placed over the trolley is 1/4 mass of Trolley .

Step by step Explanation :

We have ,

• Mass of Trolley = m
• Initial Velocity of trolley= v

Let mass of body be M , after gently placed over the trolley , trolley velocity decreases by 20% .

Thus ,

Velocity of trolley & body system

V = v-20% of v

= v-0.2v

=0.8v

As no external force acts on the system

So According to the law of conservation of Momentum .

Intital momentum = Final momentum

$\sf\:m\times\:v=(m+M)V$

$\sf\implies\:m\times\:v=(m+M)0.8v$

$\sf\implies\:m=0.8m+0.8M$

$\sf\implies\:m-0.8m=0.8M$

$\sf\implies\:0.2m=0.8M$

$\sf\implies\:M=\dfrac{0.2m}{0.8}$

$\rm\implies\:M=\dfrac{m}{4}$

______________

More About the topic :

• Conservation of Momentum :

If no external force acts on the system of constant mass the total momentum of the system remains constant .

Answer 2

Answer:

Solution :

Mass of the body placed over the trolley is 1/4 mass of Trolley .

Step by step Explanation :

We have ,

Mass of Trolley = m

Initial Velocity of trolley= v

Let mass of body be M , after gently placed over the trolley , trolley velocity decreases by 20% .

Thus ,

Velocity of trolley & body system

V = v-20% of v

= v-0.2v

=0.8v

As no external force acts on the system

So According to the law of conservation of Momentum .

Intital momentum = Final momentum

\sf\:m\times\:v=(m+M)Vm×v=(m+M)V

\sf\implies\:m\times\:v=(m+M)0.8v⟹m×v=(m+M)0.8v

\sf\implies\:m=0.8m+0.8M⟹m=0.8m+0.8M

\sf\implies\:m-0.8m=0.8M⟹m−0.8m=0.8M

\sf\implies\:0.2m=0.8M⟹0.2m=0.8M

\sf\implies\:M=\dfrac{0.2m}{0.8}⟹M=

0.8

0.2m

\rm\implies\:M=\dfrac{m}{4}⟹M=

4

m

______________

More About the topic :

• Conservation of Momentum :

If no external force acts on the system of constant mass the total momentum of the system remains constant .