A system of two blocks and a light string are kept on two inclined force (rought) as shown in figure All the are mentioned in the diagram pulley is light and frictionless `(Take g = 10ms^(-2) , sin 37^(@) = 3//5)`

If a system moving in such away that a block of `10 kg` is comming down inclined with a speed of `2 ms^(-2)`then how much time the system takes to come to a stop? [Assume the length of incline to be large enough]

Options

A. `13.33s`
B. `80s`
C. Infinite
D. Question is irrelevant

Answer

a

Explanation

As it is given that system is moving initaily in a specific dorection it mean direction a knowans it is kinetic in nature
`a = (10g sin 37^(@)- 5 sin 37^(@)- f_(1) - f_(2))/(15)`
`f_(1) = mu_(k_1)xx g sin 37^(@)= 20.0`
`f_(2)= mu_(k_2)xx5 g sin 37^(@)=2.25 `
`(2.25)/(15) = ms^(-1)`

so the required time
`t_(0) = (2)/(2.25//15)= (30)/(1.25)= 13.33s`