A body is dropped from a height of 20 metres with zero initial momentum; calculate its mass if it hits the ground with momentum 40 kg.m/s. (Assume the acceleration due to gravity 'g' = 10 m/s²)

Correct option is A

The correct answer is: (a) 2 kg

Explanation:
We can use the formula for the momentum of the body at the moment just before it hits the ground:
Momentum=m⋅v

Where:

• m is the mass of the body
• v is the final velocity of the body just before hitting the ground.

To find vvv, we use the equation of motion under gravity:
v²=u²+2gh
Since the initial velocity u=0 (the body is dropped), we get:
v²=2⋅10⋅20
$$​v ^2 = \sqrt{400} = 20 \, \text{m/s}$$​​

Now, using the momentum formula:
40=m⋅20
m=$$= \frac{40}{20} = 2 \, \text{kg}$$​​

Information Booster:

• Momentum is the product of mass and velocity: p=m⋅v
• Velocity upon hitting the ground is determined using the free fall equation, where the body gains speed under the constant acceleration due to gravity.
• The body falls a height of 20 meters, gaining speed due to gravity.