Linear Momentum and Kinetic Energy:

Linear momentum is a vector quantity that describes the motion of an object. It is defined as the product of an object's mass and its velocity. The formula for linear momentum is:

Linear Momentum = mass × velocity

On the other hand, kinetic energy is a scalar quantity that represents the energy possessed by an object due to its motion. It is defined as the work needed to accelerate an object from rest to its current velocity. The formula for kinetic energy is:

Kinetic Energy = 0.5 × mass × velocity^2

Effect of Increasing Linear Momentum:

When the linear momentum of an object is increased, it means that either the mass or velocity or both have increased. Let's consider the case where only the velocity of the object is increased while the mass remains constant.

If the linear momentum is increased by 50%, it means that the new linear momentum is 1.5 times the original linear momentum. Mathematically, we can express this as:

New Linear Momentum = 1.5 × Original Linear Momentum

Since linear momentum is given by the product of mass and velocity, we can write:

mass × New Velocity = 1.5 × (mass × Original Velocity)

Simplifying the equation, we get:

New Velocity = 1.5 × Original Velocity

Effect on Kinetic Energy:

Now, let's examine the effect of this increase in velocity on the kinetic energy of the object. Recall that kinetic energy is proportional to the square of the velocity. Therefore, if the velocity is increased by a factor of 1.5, the kinetic energy will increase by the square of that factor:

New Kinetic Energy = 0.5 × mass × (1.5 × Original Velocity)^2

Simplifying the equation, we get:

New Kinetic Energy = 0.5 × mass × (2.25 × Original Velocity^2)

New Kinetic Energy = 2.25 × (0.5 × mass × Original Velocity^2)

New Kinetic Energy = 2.25 × Original Kinetic Energy

The new kinetic energy is 2.25 times the original kinetic energy. This increase corresponds to a 125% increase, which is option 'B' in the given choices.

Conclusion:

When the linear momentum is increased by 50%, the kinetic energy increases by 125%. This result is obtained by considering the relationship between linear momentum and kinetic energy, and the fact that kinetic energy depends on the square of the velocity.