Question

Let two bodies be with masses 2kg and 5kg respectively. Let these bodies be at rest with the same force acting on them. Calculate the ratio of times that is required by both the bodies to reach the final velocity.

25:4

5:3

2:5

None
It's too urgent please answer fast​

Answer 1

Given : Let two bodies be with masses 2kg and 5kg respectively. Let these bodies be at rest with the same force acting on them.

To find : Calculate the ratio of times that is required by both the bodies to reach the final velocity.

Solution :

1. Force (1) = F/2.
2. Force (2) = F/5.

Applying formula :

★ v = u + at.

Calculations :

• Finding the ratio for both the forces.

→ v1 = F/2 × T1

→ v2 = F/5 × T2

Using above values :

→ F/2 × T1 = F/5 × T2

→ v1 : v2

→ 2 : 5

Therefore, 2:5 is the required ratio of times this is required to both the bodies to reach the final velocity.

Answer 2

Given : Two bodies be with masses 2kg and 5kg

            Bodies be at rest with the same force acting on them.

To Find :

Explanation:

Impulse on the body is

Impulse = m.∆v

$\[F{\text{ }} \times {\text{ }}t{\text{ }} = {\text{ }}m\left( {{v_2}{\text{ }} - {\text{ }}{v_1}} \right)\]$

 where,

    F = Force on the body

    t = Time

    m = mass of the body.

    $\[{{v_2}}\]$ = Final velocity

     $\[{{v_1}}\]$ = Initial velocity

Putting all value in equation for mass $\[{m_1}\]$ = 2kg at $\[{t_1}\]$

 $\[F \times {t_1} = {m_1}({v_2} - {v_1})\]$ = $\[{m_1}{v_2}\]$             ($\[{v_1}\]$=0 as initially body is at rest)

Putting value in $\[{m_2}\]$ = 5kg at $\[{t_2}\]$

 $\[F \times {t_2} = {m_2}({v_2} - {v_1})\]$ = $\[{m_2}{v_2}\]$              ($\[{v_1}\]$=0 as initially body is at rest)

Thus,

$\[\left( {\frac{{Ft1}}{{Ft2}}{\text{ }}} \right){\text{ }} = {\text{ }}\left( {\frac{{{m_1}v{\text{ }}}}{{{m_2}v}}} \right)\]$                               (Given : F is same for both bodies)

Then,

$\[\left( {\frac{{t1}}{{t2}}{\text{ }}} \right){\text{ }} = {\text{ }}\left( {\frac{{{{\text{m}}_1}{\text{ }}}}{{{m_2}}}} \right)\]$                                   ( Final velocity is same as given)

$\[\left( {\frac{{t1}}{{t2}}{\text{ }}} \right){\text{ }} = {\text{ }}\left( {\frac{2}{5}} \right)\]$

Hence ratio of times that is required by both the bodies to reach the final velocity is 2:5.