Block M slides down on frictionless incline as shown. if the minimum friction coefficient so that m does not slide with respect to M is μ then find the value of 4×μ
Physics · Mixed Chapter
JEE Mains

Question

Block M slides down on frictionless incline as shown. if the minimum friction coefficient so that m does not slide with respect to M is μ then find the value of 4×μ

G1 Physics · Accepted Answer

Step 1: The large block M slides without friction down a 37° incline, so its acceleration along the incline is a=g sin37°. Step 2: In the accelerating frame of M, the small block m feels a pseudo force opposite that acceleration. Resolve its effective weight and pseudo force relative to the horizontal contact surface of M. Step 3: Required horizontal static friction magnitude is f=m g sin37° cos37°, while normal reaction is N=m g cos²37°. Step 4: Minimum μ=f/N=tan37°=3/4. Hence 4μ=3. Answer: 3.