A man of mass 50 kg is standing on a platform of mass 30 kg kept on a horizontal surface. Mass of block is 160 kg. Distance between block and pulley ‘P’ is 6 m. There is no friction between block and platform. Man pulls the string with constant force 40 N.
(i) Assuming no friction between platform and surface time taken by block to reach pulley–
Text Solution
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(i) : Free body diagram of block –
∴ a = 
= 1 m/s 2 Free body diagram (platform + mass) system –
Assuming no friction between platform and surface
∴ a = 
= 2 m/s
2 Relative acceleration of pulley and block = 3 m/s
2 ∴ Time taken by block to reach pulley is given by
t = 
= 2 sec
(ii) : Length of string pulled out in 1 sec = 4 × distance moved by block relative to pulley
4 × 1.5 = 6 m
(iii) : Assuming friction between platform and surface
f ′ = 160
⇒ μ . N ′ ≥ 160
⇒ μ ≥ 
= 
= 0.066
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