A uniform chain of mass 2 kg hangs from a light pulley with unequal lenghts of the chain hanging from the two sides of the pulley. The force exerted by the moving chain on the pulley is

Options

A. 20 N
B. `gt20 N`
C. `lt20 N`
D. None

Answer

C

Explanation

`M=2kg.M_(0)gt(M)/(2)`
`a=(M_(0)g-(M-M_(0))g)/(M)`
`=((2M_(0)-M)g)/(M)`

`M_(0)g-T=M_(0)a`
`T=M_(0)(g-a)`
`=M_(0)g[1-((2M_(0)-M))/(M)]`
`=2M_(0)g(1-(M_(0))/(M))`

Reaction on pulley
`R=2T=4M_(0)g(1-(M_(0))/(M))`
Let `M_(0)=(3M)/(4)`
`R=4xx(3M)/(4)g(1-(3)/(4))=(3Mg)/(4)=Mg`
`M=2kg`
`Rlt(Mg=20N)`