The work done by the force acting on an object is zero if the displacement of the object
- (a)is in the opposite direction of the direction of force
- (b)is in the same direction of the direction of force
- (c)is in perpendicular direction of the direction of force
- (d)none of above
Correct — C, displacement perpendicular to the force. Work is W = F x s x cos(theta), where theta is the angle between the force and the displacement. When the displacement is perpendicular to the force, theta = 90 degrees and cos 90 = 0, so the work done is exactly zero — the force does no work even though it acts on the moving object (for example, gravity on a body moving horizontally, or the centripetal force on a body in circular motion).
- (a)is in the opposite direction of the direction of force — Here theta = 180 degrees and cos 180 = -1, so W = -F x s. This is maximum NEGATIVE work (as when friction opposes motion), not zero.
- (b)is in the same direction of the direction of force — Here theta = 0 degrees and cos 0 = +1, so W = +F x s. This is maximum POSITIVE work, not zero.
- (d)none of above — Incorrect, because option (c) is a genuine, correct condition for zero work — a displacement perpendicular to the force.
Work done by a constant force is the dot product W = F.s = F x s x cos(theta), where theta is the angle between the force and the displacement. The cosine factor means only the component of force ALONG the displacement does work. Work is maximum positive at theta = 0 degrees, maximum negative at theta = 180 degrees, and zero at theta = 90 degrees.
Read the question as 'when is cos(theta) = 0?'. The cosine vanishes only at 90 degrees, so the displacement must be perpendicular to the force. Classic examples of zero work are a satellite in a circular orbit (gravity/centripetal force stays perpendicular to the velocity), a porter carrying a load on his head while walking horizontally (weight is vertical, motion is horizontal), and the normal reaction on a body sliding along a floor.
- W = F x s x cos(theta); the work is zero when theta = 90 degrees (force perpendicular to displacement).
- Work is maximum positive at theta = 0 degrees and maximum negative at theta = 180 degrees.
- The centripetal force does zero work — it is always perpendicular to the velocity in circular motion.
- Work is a scalar quantity; its sign is decided by cos(theta).
Only a displacement at right angles to the force gives zero work.
- Assuming a force acting on a moving body must do work — a perpendicular force does none.
- Mixing up theta = 0 (maximum positive work) with theta = 180 (maximum negative work).
Work is asked as 'when is work zero/negative' or through the porter/satellite example — always return to W = F x s x cos(theta).
A simple machine helps a person doing
- (a) less work.
- (b) the same amount of work with lesser force.
- (c) the same amount of work.
- (d) the same amount of work much faster.
Answer(b) the same amount of work with lesser force.
Same underlying quantity — mechanical work (force x distance). There a simple machine keeps the total work fixed while reducing the force needed; here the work is zero because the force has no component along the displacement. Both test the definition of work, W = F.s.
- practice — not a real PYQ
A porter carries a load on his head and walks on a horizontal platform. The work done by the force of gravity on the load is
- (a)positive
- (b)negative
- (c)zero
- (d)infinite
Answer(c) zero — the horizontal displacement is perpendicular to the vertical force of gravity.
- practice — not a real PYQ
The work done by the centripetal force on a body moving uniformly in a circle is
- (a)maximum
- (b)positive
- (c)negative
- (d)zero
Answer(d) zero — the centripetal force is always perpendicular to the displacement/velocity.