A body of mass 10kg moving with velocity 30m/s collide with another body of mass 15kg.If the velocity of both the body are same after collision.Then find their common velocity.

The law of conservation of linear momentum will allow you to solve this problem. They apparently want you to assume that the 15 kg body is initially stationary.

M1*V1 = (M1 + M2)*V2
M1 = 10 kg
M2 = 15 kg
V1 = 30 m/s
Solve for V2.

star mark stands for what

* means multiplication (x)

10*30=(10+15)*V2

300/25 =25V2/25

V2=12m/s

Question

To find the common velocity of the bodies after collision, we can use the concept of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is defined as the product of its mass and velocity. Therefore, the momentum of the 10kg body before the collision is given by:
Momentum of 10kg body (before collision) = Mass × Velocity
= 10kg × 30m/s
= 300kg⋅m/s

Similarly, the momentum of the 15kg body before the collision is given by:
Momentum of 15kg body (before collision) = Mass × Velocity
= 15kg × Unknown velocity

Since the velocity of both bodies is the same after the collision, we can denote the common velocity as 'v'. Therefore, the momentum of the 15kg body after the collision is given by:
Momentum of 15kg body (after collision) = Mass × Velocity
= 15kg × v

According to the conservation of momentum principle, the total momentum before the collision is equal to the total momentum after the collision. Therefore,
Momentum before collision = Momentum after collision

(300kg⋅m/s) + (15kg × Unknown velocity) = (10kg × Common velocity) + (15kg × Common velocity)

Simplifying the equation:
300 + 15 × Unknown velocity = 10 × Common velocity + 15 × Common velocity
300 + 15 × Unknown velocity = 25 × Common velocity

Grouping like terms:
15 × Unknown velocity - 25 × Common velocity = -300

To find the common velocity, we need to solve this equation. Since we do not know the value of the unknown velocity, we cannot find the exact value of the common velocity at this point. However, we can proceed further by assuming that the unknown velocity is equal to the common velocity.

15 × Common velocity - 25 × Common velocity = -300
-10 × Common velocity = -300
Common velocity = -300 / -10
Common velocity = 30 m/s

Hence, assuming the unknown velocity is equal to the common velocity, the common velocity of both bodies after the collision is 30 m/s.