A force of (3ˆi + 4ˆj)N acts on a body and displaced it by (3ˆi + 4ˆj)m . The work done by the force is
By Definition of Work ,
Work Done = F.S= (3ˆi + 4ˆj).(3ˆi + 4ˆj)= 9+16 =25 J
When the bob of a simple pendulum swings, the work done by tension in the string is
As Angle between tension force and displacement is 90°. Work done is zero
Assertion: Work done by a force depends on frame of reference.
Reason: Force and displacement both depend on frame of reference.
Work done depends on the frame of reference because displacement depends on the frame of reference. However, real forces do not depend on the frame of reference. Hence, the Assertion is true but the Reason is false.
A force \( \vec{F} = (3x\hat{i} + 4\hat{j})\text{ Newton} \) (where \( x \) is in metres) acts on a particle which moves from a position \( (2\text{ m}, 3\text{ m}) \) to \( (3\text{ m}, 0\text{ m}) \). Then the work done is:
The work done by the force is \( W = \int_{2}^{3} 3x \, dx + \int_{3}^{0} 4 \, dy = \left[ \frac{3x^2}{2} \right]_2^3 + [4y]_3^0 = 7.5 - 12 = -4.5\text{ J} \).