Question

Two buses are moving with same kinetic energy and their masses are in the ratio 1 : 2. The ratio
of their velocities is [ ]
Two buses are moving with same kinetic energy and their masses are in the ratio 1 : 2. The ratio
of their velocities is [ ]

Answer 1

Answer :

• Ratios of velocities is √2:1

Explanation :

• Kinetic energy of buses are same
• Their mass is in ratio of 1:2

We know that,

$\longrightarrow \sf{K.E_1 \: = \: K.E_2 \: \: \: \: \: \: \: ...(1)}$

Also,

$\longrightarrow \sf{\dfrac{m_1}{m_2} \: = \: \dfrac{1}{2}} \\ \\ \longrightarrow \sf{m_2 \: = \: 2m_1 \: \: \: \: \: \: ...(2)}$

From (1),

$\longrightarrow \sf{\dfrac{K.E_1}{K. E_2} \: = \: \dfrac{\dfrac{1}{2}m_1 (v_1)^2 }{\dfrac{1}{2} m_2 (v_2) ^2}}$

Substitute value of m₂ from (2)

$\longrightarrow \sf{\dfrac{K.E_1}{K.E_2} \: = \: \dfrac{m_1 (v_1)^2}{2m_1 (v_2 ) ^2}} \\ \\ \longrightarrow \sf{1 \: = \: \dfrac{(v_1) ^2}{2( v_2 )^2}} \\ \\ \longrightarrow \sf{2 \: = \: \dfrac{(v_1)^2 }{(v_2 )^2}} \\ \\ \longrightarrow \sf{\dfrac{v_1}{v_2} \: = \: \dfrac{\sqrt{2}}{1}} \\ \\ \underline{\underline{\sf{Ratio \: of \: velocities \: is \: \sqrt{2} : 1}}}$

Answer 2

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