The weight of an object is due to
- (a)the net force acting on it.
- (b)the total of all forces acting on it irrespective of their directions.
- (c)the force that it exerts on the ground.
- (d)its inert property.
Correct — C, the force that it exerts on the ground. Weight is measured by weighing, and what a weighing machine registers is the push the body makes on the surface supporting it. Read that way — the operational definition — the weight of an object is the force it exerts on its support, and that is the sentence this option gives. The reading matches the pull of gravity, mg, whenever the body is at rest on a firm floor, because the floor pushes up with as much force as the body presses down. It comes apart in free fall: an astronaut in orbit is still pulled by gravity but presses on nothing, and the scale under them reads zero, which is exactly what 'weightless' means in that phrase. Set against the three alternatives here, only this one describes an actual force that a body has by virtue of gravity.
- (a)the net force acting on it. — The net force on a book lying on a table is zero, because the table pushes up as hard as gravity pulls down. The book still has weight, so weight cannot be the net force.
- (b)the total of all forces acting on it irrespective of their directions. — Forces are vectors and are added with their directions, never as bare numbers. A quantity found by ignoring direction is not a physical force at all.
- (d)its inert property. — Inertia is the property that resists a change of motion, and it is measured by mass, not weight. Mass stays the same everywhere; weight changes with the strength of gravity, which is why a 100 kg body still has 100 kg of mass on the Moon while weighing about a sixth as much.
Textbooks carry two definitions of weight side by side. The gravitational definition, adopted by the General Conference on Weights and Measures in 1901 and used by Indian school texts, makes weight the force of gravity on the body, W = mg. The operational definition makes weight the force measured by the act of weighing — the force the body exerts on its support. The two agree for a body resting on the ground and part company in free fall, where the first is unchanged and the second is zero.
It is worth being open about the tension here. If a candidate has learnt weight as 'the force with which the Earth attracts a body', none of the four options states that in so many words, and the key's choice of (c) is the operational reading rather than the gravitational one. The key stands, and the option can still be reached honestly by elimination: (a) fails because the net force on a resting body is zero, (b) fails because forces cannot be added without regard to direction, and (d) describes mass rather than weight. That leaves the one option naming a real downward force, and it is also the one that matches what a weighing machine does. Carry both definitions and the two ideas that come with them — apparent weight in a lift and weightlessness in orbit both belong to the operational reading.
- The gravitational definition gives weight as the product of mass and the acceleration due to gravity, W = mg.
- The operational definition gives weight as the force measured by weighing — the force the body exerts on its support.
- The two agree for a body at rest on the ground, where the support pushes back with an equal force.
- In free fall the operational weight is zero although gravity still acts, which is why astronauts in orbit float.
- Mass measures inertia and does not change with location; weight does, falling to about one-sixth on the Moon.
- Treating weight as the net force; for a body at rest the net force is zero and the weight is not.
- Confusing weight with mass, which is the inert property and does not change from place to place.
- Adding forces without their directions, which is what option (b) proposes.
As a definition item on weight, or as an applied one on what a weighing machine reads in a moving lift or in orbit.
The mass of a body on Earth is 100 kg (acceleration due to gravity, gₑ = 10 m/s²). If acceleration due to gravity on the Moon = gₑ/6, then the mass of the body on the moon is
- (a) 100/6 kg
- (b) 60 kg
- (c) 100 kg
- (d) 600 kg
Answer(c) 100 kg
The distinction option (d) gets wrong, tested directly. Moving a body to the Moon leaves its mass untouched and cuts its weight to about a sixth, which is why the 'inert property' belongs to mass and cannot define weight.
The acceleration due to gravity at the Earth's surface depends on
- (a) its mass only.
- (b) its radius only.
- (c) both its mass and radius.
- (d) either its mass or its radius.
Answer(c) both its mass and radius.
What decides the g that turns mass into weight. Because the acceleration due to gravity at a planet's surface depends on both its mass and its radius, the same body weighs different amounts on different worlds while remaining the same body.
- practice — not a real PYQ
A body of mass 60 kg is taken from the Earth to the Moon, where the acceleration due to gravity is about one-sixth of its value on Earth. On the Moon the body's
- (a)mass and weight both become one-sixth
- (b)mass stays 60 kg and weight falls to about one-sixth
- (c)mass falls to 10 kg and weight stays the same
- (d)mass and weight both stay the same
Answer(b) mass stays 60 kg and weight falls to about one-sixth — mass is the amount of matter and does not change, while weight depends on the local acceleration due to gravity.
- practice — not a real PYQ
An astronaut in a spacecraft orbiting the Earth appears weightless because
- (a)there is no gravity at that height
- (b)the astronaut and the spacecraft are in free fall together, so the astronaut presses on nothing
- (c)the spacecraft is beyond the Earth's atmosphere
- (d)the astronaut's mass has become zero
Answer(b) the astronaut and the spacecraft are in free fall together, so the astronaut presses on nothing — gravity is still acting and is what holds the craft in orbit.