Question

A ball of mss 10g is moving with a momentum of 0.5kgms .on applying a constant force on the ball for 2secs it acquires a momentum of 0.7 kg msec calculate the magnitude of the force applied and the acceleration of the ball

Answer 1

Magnitude of force applied on ball is 0.1 N and acceleration of ball is 10 m/s²

Solution

We have mass of ball(m) = 10g

m = 10/1000 kg

∴ m = 0.01 kg

We have initial momentum(p) = 0.5 kg m/s

We know that,

● Initial momentum(p) = mu

Here, m = mass, u = initial velocity.

⇒ 0.5 = 0.01 × initial velocity (u)

⇒ u = 0.5/0.01

⇒ u = 50 m/s

∴ Initial velocity of ball(u) = 50 m/s

We have, final momentum (p') = 0.7 kg m/s

We know that,

● Final momentum (p') = mv

Here, m = mass & v = final velocity.

⇒ 0.7 = 0.01 × Final velocity (v)

⇒ v = 0.07/0.01

⇒ v = 70 m/s

∴ Final velocity of ball (v) = 70 m/s

Now we have time (t) = 2 seconds.

u = 50 m/s, v = 70 m/s

☢ Using 1st equation of motion :

● v = u + at

⇒ 70 = 50 + a × 2

⇒ 2a = 70 - 50

⇒ 2a = 20

⇒ a = 20/2

⇒ a = 10 m/s²

∴ Acceleration of ball (a) = 10 m/s² (Ans.)

Now we have mass(m) = 0.01 kg

Acceleration (a) = 10 m/s²

☢ Using Newton's 2nd law :

● Forceₙₑₜ = Mass × Acceleration

⇒ Forceₙₑₜ = 0.01 × 10

⇒ Forceₙₑₜ = 0.1 N

∴Magnitude of force applied = 0.1 N (Ans.)