Correct Answer - Option 1 : 25rd s
-2
Concept:
Torque:
- It is a type of twisting force that causes the rotation of an object.
-
Torque is the measure of force that can cause an object to rotate.
- It is also called the moment of force.
- Torque is the product of the force (F) and the perpendicular distance of force from point of rotation(S).
- It is given by the formula:
- Torque is also defined as the product of a moment of inertia and angular acceleration.
τ = F × S
Where τ is t
or
τ = I × α
I is moment of inertia, α is torque
Moment of Inertia:
- Moment of inertia is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation.
- It is defined for an axis.
- The moment of inertial of a particle m at distance r from the axis is
I = mR2
- Moment of inertia of hollow sphere is mr2.
Angular acceleration:
- The angular acceleration is defined as rate of change of angular momentum.
- It is the same as acceleration in linear motion.
Calculation:
Force applied F = 50 N
Mass m = 3 kg
radius r = 40 cm = 0.4 m
Torque τ = F × r =50 N × 0.4m = 20 N m
Moment of inertia I = mr2 = 3 kg × 0.4 m × 0.4 m = 0.48 kg m2
Angular acceleration α = τ \ I = 20 N m / 0.48 = 41.66 rad / s2
Note: According to official answer of UP PGT, the answer is 25rd s-2 which will come if we consider force as 30 N.