Sumit and Sachin went for a trek and during the journey they visited a cottage. They suspended their bags to the two ropes hanging from P and Q on a wheel capable of rotating around O. Sumit suspended his bag to the rope Q and Sachin suspended his bag from the rope P. The wheel remained in equilibrium.
(a) State with a reason who is carrying a heavier bag.
(b) Based on the principle of moments, write a mathematical relation that can be used to determine the weight (W) of Sachin's bag, given that the weight of Sumit's bag is 18 kgf.
Show SolutionHide Solution↓
(a) At equilibrium clockwise moment = anticlockwise moment
Moment = force x perpendicular distance
Wt. of Sachin's bag x OP = Wt. of Sumit's bag x OR
As OR < OP. Hence, Wt. of Sumit's bag > Wt. of Sachin's bag.
Hence, Sumit's bag is heavier than Sachin's bag
(b) Given,
Wt. of Sumit's bag = 18 kgf
Let wt. of Sumit's bag be W
At equilibrium,
Clockwise moment = Anticlockwise moment
W x OP = 18 x OR
W = $\frac{18 \times \text{OR}}{\text{OP}}$