Question

A block of mass 200 g moving in x direction with a constant speed of 30 ms^-1, is subjected to a retarding force F = 0.1x J/m during its travel from x = 10 m to 20 m. Its final KE will be ____________.

Options

• 75 J

• 175 J

• 50 J

• 105 J

Answer 1

A block of mass 200 g moving in x direction with a constant speed of 30 ms^-1, is subjected to a retarding force F = 0.1x J/m during its travel from x = 10 m to 20 m. Its final KE will be 75 J.

Explanation:

Using Work-Energy Theorem,

`"W" = 1/2"m" ("v"^2 - "u"^2)`

`therefore  "Final K.E .,"`

`1/2"mv"^2 = "W" + 1/2"mu"^2`

`= -0.1 int_10^20 "xdx" + 1/2 xx 0.2 xx 30^2   (because "W" = vec"F". vec"s")`

(Negative sign indicates retardation)

`= -0.1 ["x"^2/2]_10^20 + 90`

` = -0.1 [20^2/2 - 10^2/2] + 90`

`= -15 + 90`

`= 75  "J"`