Question

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)

• A. 2 kg
• B. 4 kg
• C. 20 kg
• D. 1 kg

Answer 1

Answer:

A. 2 kg

* Initial height (h) = 20 m * Initial velocity (u) = 0 m/s (dropped with zero initial momentum) * Final momentum (p) = 40 kg·m/s * Acceleration due to gravity (g) = 10 m/s² * Mass (m) = ? Step 1: Find the final velocity when the body hits the ground Using the equation of motion: v² = u² + 2gh Where: * v = final velocity * u = initial velocity = 0 m/s * g = 10 m/s² * h = 20 m v² = 0² + 2 × 10 × 20 v² = 400 v = 20 m/s Step 2: Calculate the mass using momentum We know that momentum (p) = mass (m) × velocity (v) Given: p = 40 kg·m/s and v = 20 m/s Therefore: 40 = m × 20 m = 40/20 m = 2 kg Answer: The mass of the body is 2 kg (Option A)