Question

A bomb at rest explodes into 3 parts of the same mass. The momentum of the two parts is `-2"P"hat"i"` and `4"P"hat"J"` respectively. The magnitude of the momentum of the third part is ______

Options

• P

• `sqrt5`P

• `sqrt20`P

• `sqrt13`P

Answer 1

A bomb at rest explodes into 3 parts of the same mass. The momentum of the two parts is `-2"P"hat"i"` and `4"P"hat"J"` respectively. The magnitude of the momentum of the third part is `underline(sqrt20"P")`.

Explanation:

Let, `vec"P"`_A = -2P`hat"i"` and `vec"P"`_B = 4P`hat"j"`

According to law of conservation of momentum,

`vec"P"_"A" + vec"P"_"B" + vec"P"_"c" = 0`

∴ `-2"P"hat"i" + 4"P"hat"j" + vec"P"_"c" = 0`

∴ `vec"P"_"c" = 2"P"hat"i" - 4"P"hat"j"`

∴ `|"P"_"C"| = sqrt(4"P"^2 + 16"P"^2) = sqrt20"P"`