Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A bullet of mass 20 g is fired from a rifle with a velocity of 800 ms –1 . After passing through a mud wall 100 cm thick, velocity drops to 100 m s -1 . What is the average resistance of the wall?
(Neglect friction due to air and work of gravity)
Text Solution
Verified by ExpertsThe correct answer is:
B
Step 1: Convert the mass of the bullet from grams to kilograms:
Mass (m) = 20 g = 0.02 kg
Step 2: Use the formula for momentum before and after passing through the wall:
Initial momentum (p_initial) = m * v_initial = 0.02 kg * 800 m/s = 16 kg m/s
Final momentum (p_final) = m * v_final = 0.02 kg * 100 m/s = 2 kg m/s
Step 3: Calculate the change in momentum (Δp):
Δp = p_final - p_initial = 2 kg m/s - 16 kg m/s = -14 kg m/s
Step 4: Calculate the time taken to pass through the wall. The average velocity while passing through the wall is taken to be the average of initial and final velocities:
Average velocity (v_avg) = (v_initial + v_final) / 2 = (800 m/s + 100 m/s) / 2 = 450 m/s
Distance (d) = 1 m (100 cm)
Time (t) = d / v_avg = 1 m / 450 m/s = 0.00222 s
Step 5: Calculate the average resistance (R) using the change in momentum and time:
R = rac{Δp}{t} = \frac{-14 kg m/s}{0.00222 s} \approx -6306.31 N
The average resistance from the wall acting against the bullet is approximately 6306.31 N.
Therefore, the average resistance of the wall is about 6300 N (approximately).
Mass (m) = 20 g = 0.02 kg
Step 2: Use the formula for momentum before and after passing through the wall:
Initial momentum (p_initial) = m * v_initial = 0.02 kg * 800 m/s = 16 kg m/s
Final momentum (p_final) = m * v_final = 0.02 kg * 100 m/s = 2 kg m/s
Step 3: Calculate the change in momentum (Δp):
Δp = p_final - p_initial = 2 kg m/s - 16 kg m/s = -14 kg m/s
Step 4: Calculate the time taken to pass through the wall. The average velocity while passing through the wall is taken to be the average of initial and final velocities:
Average velocity (v_avg) = (v_initial + v_final) / 2 = (800 m/s + 100 m/s) / 2 = 450 m/s
Distance (d) = 1 m (100 cm)
Time (t) = d / v_avg = 1 m / 450 m/s = 0.00222 s
Step 5: Calculate the average resistance (R) using the change in momentum and time:
R = rac{Δp}{t} = \frac{-14 kg m/s}{0.00222 s} \approx -6306.31 N
The average resistance from the wall acting against the bullet is approximately 6306.31 N.
Therefore, the average resistance of the wall is about 6300 N (approximately).
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