Question

If the object has the momentum is 20 and kinetic energy is 40. Than find the mass of the object

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Mass\:of\:object=5\:kg}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Linear \: momentum(p) = 20\:kg\:m/s \\ \\ \tt: \implies Kinetic \: energy(K.E) = 40 \: joule \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Mass\: of \: object(m)= ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Kinetic \: energy = \frac{1}{2} m {v}^{2}$

$\tt: \implies \frac{40 \times 2}{m} = {v}^{2} \\ \\ \tt: \implies v = \sqrt{ \frac{80}{m} } - - - - - (1) \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Linear \: momentum = mv \\ \\ \tt: \implies 20 = mv \\ \\ \tt: \implies 20 = m \times \sqrt{ \frac{80}{m} } \\ \\ \text{Squaring \: both \: side} \\ \\ \tt: \implies {20}^{2} = {m}^{2} \times (\sqrt{ \frac{80}{m} } )^{2} \\ \\ \tt: \implies 400 = {m}^{2} \times \frac{80}{m} \\ \\ \tt: \implies \frac{400}{80} = m \\ \\ \green{\tt: \implies m = 5 \: kg} \\ \\ \green{\tt \therefore Mass \: of \: object \: is \: 5 \: kg}$