Question

A wedge of mass M = 4m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by ______.

Options

• `"v"^2/"g"`

• `(2"v"^2)/(7"g")`

• `(2"v"^2)/(5"g")`

• `"v"^2/(2"g")`

Answer 1

A wedge of mass M = 4m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by `bb((2"v"^2)/(5"g"))`.

Explanation:

mv = (m + M)V'

or v = `"mv"/("m"+"M")="mv"/("m"+4"m")="v"/5`

Using conservation of ME, we have

`1/2"mv"^2=1/2("m"+4"m")("v"/5)^2+"mgh"`

or h = `2/5 "v"^2/"g"`