Question

A force of 20 N acts on a body at rest for a time of 2 s and then a force of 60 N acts for a time of 1.5 s in the opposite direction. If the final velocity of the body is 10 m/s in the direction of the 60 N force, then the mass of the body is:

• A. \( 10 \text{ kg} \)
• B. \( 8 \text{ kg} \)
• C. \(\mathbf{5 \text{ kg}}\)
• D. \( 16 \text{ kg} \)

Hint:

When dealing with impulse-momentum problems: - Use \( I = F \cdot t \) to calculate impulse. - Consider direction carefully (impulse values are positive in one direction and negative in the opposite). - Apply the momentum equation \( m v = \sum \text{Impulses} \) to find unknowns.

Answer 1

The Correct Option is C

Step 1: Applying the impulse-momentum theorem The impulse-momentum theorem states: \[ \text{Impulse} = \text{Change in Momentum} \] Impulse is given by: \[ \text{Impulse} = F \cdot t \] Let \( m \) be the mass of the body.

 Step 2: Calculating momentum changes 1. Impulse due to 20 N force (First phase) - Force \( F_1 = 20 \) N - Time \( t_1 = 2 \) s Impulse: \[ I_1 = F_1 \cdot t_1 = 20 \times 2 = 40 \text{ Ns} \] Since the body starts from rest, initial momentum: \[ \text{Initial momentum} = 0 \] Momentum after first phase: \[ p_1 = 40 \text{ Ns} \] 2. Impulse due to 60 N force (Second phase in opposite direction) - Force \( F_2 = 60 \) N - Time \( t_2 = 1.5 \) s Impulse: \[ I_2 = F_2 \cdot t_2 = 60 \times 1.5 = 90 \text{ Ns} \] Since this force acts in the opposite direction, it reduces momentum. 

Step 3: Using final velocity condition Final momentum after second phase: \[ m \cdot v = 90 - 40 = 50 \text{ Ns} \] Given that the final velocity \( v = 10 \) m/s: \[ m \cdot 10 = 50 \] Solving for \( m \): \[ m = \frac{50}{10} = 5 \text{ kg} \]

 Step 4: Verifying the correct option Comparing with the given options, the correct answer is: \[ \mathbf{5 \text{ kg}} \]