\( 16 \text{ kg} \)
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: \[ \mathbf{5 \text{ kg}} \]
The products of the following reactions \( X \) and \( Y \) respectively are Reaction:
What are the reagents A, B, and C respectively in the following reaction sequence? Reaction Sequence:
Chemical Compounds
A: CH3CH2CHO
B: CH3COCH3
D: