Question

8. Calculate the KE of a ball of mass 100gm and
momentum 1000gm-cm/s​

Answer 1

GIVEN

Mass of the ball, m = 100 g

Momentum, p = 1000 g cm/s

TO FIND

Kinetic energy of the ball,K

FORMULA

Kinetic energy, K = mv²/2

Momentum, p = mv

SOLUTION

STEP 1 : TO FIND VELOCITY

p = mv

v = p/m

v = 1000/100

v = 10 cm/s

THE VELOCITY OF THE BALL IS 10 cm/s

STEP 2: TO FIND KINETIC ENERGY

K = mv²/2

$k = \dfrac{m {v}^{2} }{2} \\ \\ k = \dfrac{100 \times {(10)}^{2} }{2} \\ \\ = \dfrac{100 \times 100}{2} \\ \\ = \dfrac{10000}{2} \\ \\ k = 5000 \: g {cm}^{2} {s}^{ - 2}$

Kinetic energy of the ball is 5000 g cm² /s²

Kinetic energy of the ball in SI unit is 5000× 10^-7

$k = 5 \times {10}^{3} \times {10}^{ - 7} \\ \\ k = 5 \times {10}^{(3 - 7)} \\ \\ k =5 \times {10}^{ - 4} \: joules$

DIRECT FORMULA:

p = √(2mk)

p² = 2mk

k = p²/ 2m

Answer 2

Question :

• Calculate the KE of a ball of mass 100gm and momentum 1000gm-cm/s ?

Given :

• Mass of ball = 10gm
• Momentum = 1000gm-cm/s

To find :

• Calculate the KE of a ball

Let's Start :

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: :\implies \sf\dfrac{100}{10} \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \sf 10 \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \sf0.1m/ sec$

Calculation :

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \sf \: K.E = \dfrac{1}{2} m {u}^{2} \\ \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \sf \dfrac{1}{2} \times \frac{10}{1000} \times ( \dfrac{1}{10} ) {}^{2} \: j \\ \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \sf0.5 \times {10}^{ - 2} \times {10}^{ - 4} \\ \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\boxed{\boxed{ \sf5 \times {10}^{ - 5} }}}$