A small block slides on a frictionless horizontal table. It is constrained to move inside a ring of radius 1m fixed to the table. At t = 0 the block is moving along the circumference inside the ring with speed 10 m/s. the coefficient of friction between block and ring is 0.1. the speed of the block at t = 1 sec is : __________ m/s
Physics · Mixed Chapter
JEE Mains

Question

A small block slides on a frictionless horizontal table. It is constrained to move inside a ring of radius 1m fixed to the table. At t = 0 the block is moving along the circumference inside the ring with speed 10 m/s. the coefficient of friction between block and ring is 0.1. the speed of the block at t = 1 sec is : __________ m/s

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Motion along the inside of a fixed ring of radius R has normal reaction N=mv²/R. Friction magnitude is μN and acts opposite the velocity. Step 2: Tangential equation m dv/dt=−μmv²/R gives dv/v²=−(μ/R)dt. Step 3: Integrate from v₀=10 m/s at t=0: 1/v−1/v₀=(μ/R)t, so v=v₀/[1+(μv₀/R)t]. Step 4: R=1 m, μ=0.1, t=1 s gives v=10/(1+1)=5 m/s. Answer: 5.