Question

A rocket with a lift-off mass $3.5 \times 10^{4}$ kg is blasted upwards with an initial acceleration of $10 \mathrm{m} / \mathrm{s}^{2}$. Then the initial thrust of the blast is-
(A) $3.5 \times 10^{5} \mathrm{N}$
(B) $7.0\times {{10}^{5}}\text{N}$
(C) $14.0 \times 10^{5} \mathrm{N}$
(D) $175 \times 10^{1} \mathrm{N}$

Answer 1

Hint
We know that thrust is defined as a mechanical force that is generated most often through the reaction between the accelerating masses of the gases that are taken into consideration. Based on this concept we have to solve this question.

Complete step by step answer
From the figure given, we can see that the force due to gravity mg acts on the rocket in the downward direction while the thrust F acts in the upward direction.

$F-m g=m a$.
By solving the above equation, we get,
$\therefore F=m(g+a)$.
Given,
Mass of rocket while lift-off (m) = $3.5 \times 10^{4}$kg
The initial acceleration of rocket while lift-off is $10 \mathrm{m} / \mathrm{s}^{2}$
Therefore, the thrust can be calculated with the equation given which evaluates to:
$=3.5+{{10}^{4}}(10+10)$
$=7\times {{10}^{5}}\text{N}$
Therefore, the correct answer is Option (B).

Note
We should know that thrust is mostly generated because of the reaction of the acceleration between the gases, but it should not be confused with acceleration. Trust is a vector quantity since it gives us an idea about the accelerating direction of the gas as well. The magnitude of the thrust depends on the amount of the gas that is accelerated and on the difference in the velocity of the gas that is passed through the engine.