Question

if momentum is increased by 100percent without changing mass what will be new velocity

Answer 1

$\textbf{\huge{\underline{ Hello Mate! }}}$

Since we know that,

Momentum = p

Velocity = v and Mass = m

p = mv1

p / m = v1

When momentum is increased 100%,

p + 100p/100 = mv

p + p = mv

2p = mv2

2p / m = v2

$\frac{v2}{v1} = \frac{ \frac{2p}{m} }{ \frac{p}{m} } \\ \frac{v2}{v1} = \frac{2p}{m} \times \frac{m}{p} \\ \frac{v2}{v1} = 2$

$\textsf{\red{ Hence velocity will increase 2 }}$

$\textbf{ Have great future ahead! }$

Answer 2

Let  the  initial momentum of  body P₁ , velocity v₁ and final momentum be  v₂.

Let the mass if  object  be  m

P₁  = mv₁ .................i)

P₂ = mv₂ ...........ii)

Given, that momentum is increased by 100 % it means,

(change in momentum/initial momentum) × 100% = 100%

$\frac{p_2-p_1}{p_1}\times100\%=100\%$

Eq. ii) ÷ Eq. i)

$\frac{p_2}{p_1}=\frac{v_2}{v_1}\\\;\\\frac{p_2}{p_1}-1=\frac{v_2}{v_1}-1\\\;\\\frac{p_2-p_1}{p_1}=\frac{v_2-v_1}{v_1}\\\;\\\frac{p_2-p_1}{p_1}\times100\%=\frac{v_2-v_1}{v_1}\times100\%\\\;\\100\%=\frac{v_2-v_1}{v_1}\times100\%\\\;\\1=\frac{v_2-v_1}{v_1}\\\;\\v_1=v_2-v_1\\\;\\v_1+v_1=v_2\\\;\\v_2=2v_1$

Hence, velocity will be  two times  of  initial velocity