First slide

Second law

Question

A force produces an acceleration of 4 m s^-2 in a body of mass m₁ kg and the same force produces an acceleration of 6 m s^-2 in another body of mass m₂. If the same force is applied to (m₁ + m₂), then the acceleration will be

Easy

A

$10 {ms}^{- 2}$
B

$2 {ms}^{- 2}$
C

$2 .4 {ms}^{- 2}$
D

$5 .4 {ms}^{- 2}$

Solution

$a_{1} = \frac{F}{m_{1}}, a_{2} = \frac{F}{m_{2}} \begin{array}{l} ∴ a_{3} = \frac{F}{m_{1} + m_{2}} = \frac{F}{F / a_{1} + F / a_{2}} = \frac{a_{1} a_{2}}{a_{1} + a_{2}} \\ = \frac{4 \times 6}{4 + 6} m / s^{2} = 2 .4 m / s^{2} . \end{array}$

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