Question

A ball of mass 0.1 kg makes an elastic head-on collision with a ball of unknown mass, initially at rest. If the 0 .1 kg ball rebounds at one-third of its original speed, the mass of the other ball is ______.

Options

• 0.1 kg

• 0.2 kg

• 0.3 kg

• 0.4 kg

Answer 1

A ball of mass 0.1 kg makes an elastic head-on collision with a ball of unknown mass, initially at rest. If the 0 .1 kg ball rebounds at one-third of its original speed, the mass of the other ball is 0.2 kg.

Explanation:

`"V"_1 = ("m"_1 - "m"_2)/("m"_1 + "m"_2) "u"_1 +(2"m"_2)/("m"_1 + "m"_2) "u"_2`

`"-u"_1/3 = (("m"_1 - "m"_2)"u"_1 + 2"m"_2"u"_2)/("m"_1+ "m"_2)`

=`((0.1 - "m"_2)"u"_1 + 2xx"m"_2 xx 0)/(0.1+ "m"_2)`

∴ `"-u"_1/3 =((0.1 - "m"_2)"u"_1)/(0.1+ "m"_2)`

∴ `-1/3 =(0.1 - "m"_2)/(0.1+ "m"_2)`

∴ `0.1 + "m"_2 = -0.3+ 3"m"_2`

∴ `2"m"_2 = 0.4`

∴ `"m"_2 = 0.2  "kg"`