Work Power And Energy

Step 1: Applying the impulse-momentum theorem The impulse-momentum theorem states: Impulse is given by: Let be the mass of the body.

Step 2: Calculating momentum changes 1. Impulse due to 20 N force (First phase) - Force N - Time s Impulse: Since the body starts from rest, initial momentum: Momentum after first phase: 2. Impulse due to 60 N force (Second phase in opposite direction) - Force N - Time s Impulse: Since this force acts in the opposite direction, it reduces momentum.

Step 3: Using final velocity condition Final momentum after second phase: Given that the final velocity m/s: Solving for :

Step 4: Verifying the correct option Comparing with the given options, the correct answer is:

Step 1: Understanding the given problem We apply the equation for the coefficient of restitution (e), which is given by: where: - and are initial velocities of the 200 g and 600 g balls respectively. - and are final velocities after the collision. - Given that the 600 g ball is initially at rest, . - The coefficient of restitution is given as .

Step 2: Applying the restitution formula Since , the equation simplifies to: Rearranging:

Step 3: Applying momentum conservation Momentum before and after collision must be equal: Substituting given values:

Step 4: Solving for and From the restitution equation: Substituting in the momentum equation: Solving for : Now, using :

Step 5: Finding the ratio Expressing as a ratio: Thus, the correct ratio is: