The moment of inertia of a body about a given axis is 1.2 kg ´ metre2. Initially, the body is at rest. In order to produce a rotating kinetic energy of 1500 joules, an angular acceleration of 25 radian/sec2 must be applied about that axis for a duration of (a) 4 sec (b) 2 sec (c) 8 sec (d) 10 sec

To determine the duration needed to produce a rotating kinetic energy of 1500 joules with an angular acceleration of 25 radian/sec², we can use the relationship between kinetic energy, moment of inertia, and angular velocity. The kinetic energy (KE) of a rotating body is given by the formula:

Understanding Rotational Kinetic Energy

The formula for rotational kinetic energy is:

KE = (1/2) * I * ω²

Where:

• KE is the kinetic energy in joules.
• I is the moment of inertia in kg·m².
• ω is the angular velocity in radians per second.

In this scenario, we know the moment of inertia (I = 1.2 kg·m²) and the desired kinetic energy (KE = 1500 joules). We need to find the final angular velocity (ω) that corresponds to this kinetic energy.

Calculating Angular Velocity

By rearranging the kinetic energy formula to solve for angular velocity, we get:

ω = sqrt((2 * KE) / I)

Now, substituting the known values:

ω = sqrt((2 * 1500) / 1.2)

ω = sqrt(2500)

ω = 50 rad/sec

Finding the Time to Reach Angular Velocity

Next, we can find the time it takes to reach this angular velocity using the equation of motion for rotational systems:

ω = α * t

Where:

• α is the angular acceleration (25 rad/sec²).
• t is the time in seconds.

Rearranging this equation gives:

t = ω / α

Now, substituting the values:

t = 50 / 25

t = 2 seconds

Final Answer

Based on the calculations, the duration required to produce a rotating kinetic energy of 1500 joules with an angular acceleration of 25 radian/sec² is 2 seconds. Therefore, the correct option is (b) 2 sec.