If the block P as shown in the figure below were to be at rest, what should the magnitude of force F be ?
- (a)5 N
- (b)6 N
- (c)8 N
- (d)10 N
Answer
Why
Correct — C, 8 N. The printed figure shows block P with five horizontal forces marked on it. Two point left: 10 N and 15 N. Three point right: 2 N, 15 N and the unknown F. 'At rest' means in equilibrium, so the forces along the line of action must cancel — the total to the left must equal the total to the right. Left: 10 + 15 = 25 N.
Right: 2 + 15 + F = 17 + F. Setting them equal: 17 + F = 25, so F = 8 N. The 15 N forces are worth noticing: one acts each way, so they cancel outright and the problem reduces to 10 = 2 + F.
Why the others are wrong
- (a)5 N — This does not balance the block — with F = 5 N the rightward total is 22 N against 25 N leftward, leaving a net 3 N and the block would accelerate.
- (b)6 N — Still 2 N short. It would follow from mistakenly taking one of the leftward forces as 8 N rather than 10 N.
- (d)10 N — This is the value of one of the leftward forces, carried over as the answer. It ignores the 2 N already acting rightward, which reduces what F has to supply from 10 N to 8 N.
Concept
A body at rest is in translational equilibrium: the vector sum of all forces on it is zero. For forces along a single line this reduces to arithmetic — the magnitudes in one direction must total the same as those in the other. Equal and opposite pairs cancel and can be struck out before any adding is done.
The figure deliberately includes a 15 N force on each side. Spotting that they cancel turns a five-force problem into 10 = 2 + F, which is worth doing because it removes two chances to mis-add. The other common slip is to treat F as having to balance the largest single opposing force rather than the net of all of them.
Key facts
- At rest means net force zero, not merely that opposing forces exist.
- For collinear forces, total one way = total the other way.
- Equal and opposite forces cancel and can be cancelled first.
- Left: 10 + 15 = 25 N. Right: 2 + 15 + F.
- F = 25 − 17 = 8 N.
Cancel the matched 15 N pair and the balance reduces to 10 = 2 + F — option (c).
Study next
Common traps
- Balancing F against a single opposing force instead of the net.
- Missing that equal and opposite forces cancel.
- Assuming 'at rest' allows a small residual net force.
NDA prints a block with several labelled arrows and asks for the unknown that holds it still — total each direction and set them equal.
Related PYQs
No directly related past PYQ was found.
Practice
- practice — not a real PYQ
A block is acted on by 12 N to the right and 5 N to the left. What additional force keeps it at rest?
- (a)7 N to the right
- (b)7 N to the left
- (c)17 N to the left
- (d)17 N to the right
Answer(b) 7 N to the left — the net is 7 N rightward, so an equal force leftward balances it. - practice — not a real PYQ
A body remains at rest under the action of three forces. This means
- (a)all three forces are equal
- (b)their vector sum is zero
- (c)two of them must be zero
- (d)they act along the same line
Answer(b) their vector sum is zero — that is the condition for equilibrium.