Question

Two bodies A and B having masses in the ratio of 3 : 1 possess the same kinetic energy. The ratio of linear momentum of B to A is:

Options

• 1 : 3

• 3 : 1

• `1: sqrt3`

• `sqrt3: 1`

Answer 1

`1: sqrt3`

Explanation:

As `1/2 "m"_"A" "v"_"A"^2 = 1/2 "m"_"B" "v"_"B"^2`

`"v"_"A"/"v"_"B" = sqrt("m"_"B"/"m"_"A")`;

`"P"_"B"/"P"_"A" = ("m"_"B" "v"_"B")/("m"_"A" "v"_"A")`

= `"m"_"B"/"m"_"A" sqrt("m"_"A"/"m"_"B")`

= `sqrt("m"_"B"/"m"_"A")`

= `1/sqrt3`