If the linear momentum is increased by 5%, the kinetic energy will increase by :(A) 50% (B) 100%(C) 125% (D) 10%

To determine the increase in kinetic energy when the linear momentum is increased by 5%, we need to understand the relationship between linear momentum and kinetic energy.

The linear momentum of an object is given by the product of its mass and velocity, while the kinetic energy is given by half the product of its mass and the square of its velocity.

Let's assume the initial linear momentum is P and the initial kinetic energy is K. When the linear momentum is increased by 5%, the new linear momentum becomes P + 0.05P = 1.05P.

Now, let's consider the relationship between linear momentum and velocity. Since linear momentum is directly proportional to velocity, a 5% increase in linear momentum corresponds to a 5% increase in velocity.

Therefore, the new velocity becomes 1.05 times the initial velocity.

Now, let's calculate the new kinetic energy. The new kinetic energy is given by half the product of the mass and the square of the new velocity.

Since the mass remains constant, the new kinetic energy is (1/2) * mass * (1.05 * initial velocity)^2.

Simplifying this expression, we get (1/2) * mass * 1.1025 * (initial velocity)^2.

Comparing this with the initial kinetic energy K, we can see that the new kinetic energy is 1.1025 times the initial kinetic energy.

Therefore, the kinetic energy will increase by 10.25% (option D) when the linear momentum is increased by 5%.