Question

Work done upon a body of mass 'm' to change its velocity from 2m/s to 5 m/s
is 210). Calculate the value of 'm'.​

Answer 1

Answer:

Given:

Change in velocity from 2 m/s to 5 m/s.

Work done = 210 Joule.

To find:

Mass of the object

Calculation:

We shall apply Work - Energy theorem to solve this problem.

Work done = change in Kinetic Energy

∴ W = ∆ KE

=> 210 = ½m(v2)² - ½m(v1)²

=> 210 = ½m(5)² - ½m(2)²

=> ½m[5² - 2²] = 210

=> ½m × 21 = 210

=> m = 20 kg.

$\boxed {mass = 20 \: kg}$

Answer 2

Answer:

${\boxed{\bold\green{Mass = 20\:kg}}}$

Explanation:

$\bf{Given}\begin{cases}\sf{Work\:done=210\:joule}\\\sf{Initial\:velocity=2\:m/s}\\\sf{Final\:velocity=5\:m/s}\\\sf{m=\:?}\end{cases}$

Formula used:-

${\boxed{\bold{Work\:done=\triangle\:Kinetic\: energy}}}$

$\rightarrow\sf 210 = \frac{1}{2}m{(V_2)}^{2} - \frac{1}{2}m{(V_1)}^{2} \\\rightarrow\sf 210 = (\frac{m}{2}\times {5}^{2})- (\frac{m}{2}\times {2}^{2}) \\\rightarrow\sf 210 = \frac{m}{2}\:(25-4) \\\rightarrow\sf 210 = \frac{21m}{2} \\\rightarrow\sf 21m = 420 \\\rightarrow\sf m =\cancel{\frac{420}{21}\:kg}$

$\rightarrow{\bold\purple{\boxed{\sf {m = 20\:kg }}}}$

$\therefore\bold{\underline{Value\:of\:m=20\:kg}}$