Question

A bullet of mass 50g is horizontally fired with a velocity200m/s. From a pistol of mass5 kg what is the recoil velocity pf the pistol

Answer 1

Answer:

Given : A gun is fired .

Mass of bullet = 50g

velocity of bullet = 200 m/s

mass of gun = 5 kg = 5000 g

To find : Recoil velocity of pistol

Pre - requisite knowledge:

Whenever a gun is fired, it follows conservation of momentum.

Formula used :

M1*V1 = - M2*V2,

where M1 is the mass of pistol, V1 I the velocity of pistol(recoil) , M2 is the mass of bullet, V2 is the velocity of bullet.

Calculations:

Putting the data available

5000*V1 = - (50*200)

=> V1 = - 2 m/s.

The recoil velocity of the pistol is 2 m/s

The negative sign indicates that the recoil velocity of the pistol is opposite in direction wrt to the velocity of the bullet.

Answer 2

$\Huge{\red{\underline{\underline{\rm{Answer}}}}}$

$\bold{\underline{\textsf{To find-Recoil\:Velocity\:of\:Pistol}}}$

NOW

$\blacksquare$ By law of conservation of momentum,the total momentum remains conserved.

$\blacksquare$ Also Action reaction is shown here in this case.

$\huge\bold</strong><strong>{\mathtt{\red{</strong><strong>O</strong><strong>n</strong><strong>\</strong><strong>:</strong><strong>Solving</strong><strong>}}}$

$\Huge</strong><strong>{\underline{\textsf{</strong><strong>m1v1</strong><strong>=</strong><strong>-</strong><strong>m2v2</strong><strong>}}}$

$\blacksquare$ Here , m1 is the mass of pistol and v1 is its recoil velocity,whereas m2 is mass of bullet and v2 is the spped with which it is fired.

CONVERSION

5 kg =5000 g

$m1v1 = - m2v2$

$5000 \times v1 = - 50\times 200$

$v1 = - \dfrac{50 \times 200}{5000}$

$v 1= - \dfrac{5\times 2}{5}$

$\Huge{\red{\underline{\underline{\rm{v1=-2\:m/s}}}}}$

HENCE RECOIL VELOCITY OF PISTOL IS -2 m/s .

$\blacksquare$ Here,negative sign indicates that the pistol moves in opposite direction when the bullet is fired.