Sample 1Medium
A block rests on a rough plank hinged at one end, forming an inclined plane. The figure shows weight mg acting down, normal reaction N perpendicular to the plank and friction f up the plank. The plank's angle with the horizontal is slowly increased, and the block just begins to slide when the angle reaches 30°. What is the coefficient of static friction?
- A
0.5
- B
0.866
- C
1.73
- D
0.577
Show the answer
The answer is D.At the point of sliding, mg sin θ = μs mg cos θ, so μs = tan 30° = 1/√3 ≈ 0.577.
- A.
0.5 is sin 30°, not tan 30°.
- B.
0.866 is cos 30°, not tan 30°.
- C.
1.73 is tan 60°, which would apply if the angle were 60°.
NCERT: Class 11 Physics, Chapter 4
Sample 2NEET level
Assertion (A): A book lying at rest on a horizontal table, with no horizontal force applied on it, experiences zero static friction. Reason (R): Static friction is self-adjusting: it equals the applied force that tends to cause relative motion, up to its limiting value μs N.
- A
Both A and R are true and R is the correct explanation of A
- B
Both A and R are true but R is not the correct explanation of A
- C
A is true but R is false
- D
A is false but R is true
Show the answer
The answer is A.Static friction opposes impending motion and adjusts itself to the applied force, up to the limit μs N. With no applied horizontal force there is no impending motion, so the static friction is zero, which is exactly what R explains.
- B.
R is the very reason A holds: since friction matches the applied force, zero applied force means zero friction.
- C.
R is true: static friction is not always μs N, only its maximum is.
- D.
A is true: with no tendency to slide, static friction is zero.
NCERT: Class 11 Physics, Chapter 4 (Laws of Motion), Friction