Question

Fig shows a pulley P; fixed on top of an inclined plane. A massless, inextensible string is wrapped around the pulley. The free end of string is attached to a block of mass 200 g as shown. μ = 0.1 is coefficient of friction between inclined plane and block. M.I of pulley about its own axis is 0.8 kgm² and its radius is 40 cm. The system is let go from rest. The mass m descends a distance of 1m along the inclined plane. What is linear speed of m? There is no slipping of string on pulley. g = 10 ms^-2 .

Answer 1

When m descends down by a distance of 1m along the plane; the vertical distance, h, is

h = 1 × cos 53° = 0.6 m

The loss in gravitational P.E of m = mgh

= 0.2 × 10 × 0.6 = 1.2 J .....(i)

The work done against force of friction between block and inclined plane 

v = linear speed of mass M; ω = angular speed of pulley. Since there is no slipping v = Rω. Therefore

From law conservation of energy