First slide

Second law

Question

A rocket of mass 100 kg burns 0.1 kg of fuel per sec. If velocity of exhaust gas is 1 km/sec, then it lifts with an acceleration of

Moderate

A

$1000 {ms}^{- 2}$
B

$100 {ms}^{- 2}$
C

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

$1 {ms}^{- 2}$

Solution

$\frac{dm}{dt} = 0 .1 kg / \sec; Mass of the rocket = 100 kg \begin{aligned} u = 1 km / \sec = 1000 m / \sec . \\ F = \frac{d (mu)}{dt} = m \frac{du}{dt} - u \frac{dm}{dt} = 0 \end{aligned}$
as the mass is decreasing $100 a - 1000 \times 0 .1 = 0$
$a = + 1 m / s^{2}$

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