Question

Which of the following has maximum momentum?

Options

• A 100 kg vehicle moving at 0.02 m s^-1

• A 4 g weight moving at 1000 cm s-¹ 

• A 200 g weight moving with kinetic energy of 10^-6 J.

• A 200 g weight after falling through one kilometer.

Answer 1

A 200 g weight after falling through one kilometer.

Explanation:

Momentum of vehicle = 100 x 0.02 = 2 kg m/s  .... (i)

Momentum of weight = `4 xx 10^-3 xx 10^3 xx 10^2`

`4 xx 10^-2` kg m/s  .... (ii)

For 200 g weight, K.E. = `1/2 "mv"^2 = 10^-6 "J"`

∴ v = `((2 xx 10^-6)/(0.2))^(1/2) = 10^(-5/2)`

Hence, its momentum ` = 0.2 xx 10^(-5/2)` kg m/s  .... (iii)

For a weight falling from b = 1 km = 10³ m

`"(P.E)"_"max" = "(K.E)"_"max"`

mgh = `1/2 "mv"^2 `

∴ v = `sqrt (2"gh") = sqrt(2 xx 9.8xx 10^3` = 140 m/s 

Henc = e, its momentum = `0.2 xx 140`

= 28 kg m/s  .... (iv)

Comparing the values, the momentum of a 200 g weight after falling through 1 km has the maximum value.