Question

A particle of mass m moving eastward with a speed v collides with another particle of the same mass moving northward with the same speed v. The two particles coalesce on collision.The new particle of mass 2 m will move in the north - easterly direction with a velocity

• A. $v/2$
• B. $2v$
• C. $v/\sqrt{2}$
• D. $v$

Answer 1

The correct option is C $v/\sqrt{2}$

From conservation of momentum

Initial momentum = final momentum

$m\times v\hat{i}+m\times v\hat{j}=(m+m)\overrightarrow{V}$

$\overrightarrow{V}=\frac{v}{2}\hat{i}+\frac{v}{2}\overrightarrow{j}$

$\left|\overrightarrow{V}\right|=\sqrt{{\left(\frac{v}{2}\right)}^2+{\left(\frac{v}{2}\right)}^2}=\frac{v}{\sqrt{2}}$

Hence, final velocity id $\frac{v}{\sqrt{2}}$