An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of `12 ms^(-1)` and the second part of mass 2 kg moves with 8 `ms^(-1)` speed. If the third part flies off with `4 ms^(-1)` speed, then its mass is

Options

A. 7kg
B. 17kg
C. 3 kg
D. 5kg

Answer

D

Explanation

The situation is as shown in the figure according to law of conservation of linear momemtum
` vecp_1 + vecp_2 + vecP_3 =0 therefore vecP_3 =- vecP_1 + vecP_(2)`
here ` vecv_1 = ( 1 kg ) ( 12 ms^(-1)) hati = 12 hati kg ms^(-)`
` therefore vecP_3 = - (12 hati + 16 hatj ) kg ms^(-1) `
The magnitude of `P_3 ` is
` P_3 = sqrt((12)^2 + (16)^2) = 20 kg ms^(-1)`
` therefore m_3 = (p_3)/(v_3) =( 20 kg ms^(-1))/(4 ms^(-1)) =5 kg `