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Question: A body is moving with a velocity \(5m{{s}^{-1}}\) along a straight line. A force of 10N is applied t...

A body is moving with a velocity 5ms−15m{{s}^{-1}} along a straight line. A force of 10N is applied to the body perpendicular to the line of motion. If the body is of mass 2kg, then the acceleration of the body along the initial straight line of motion is:
A. 5ms−25m{{s}^{-2}}
B. 0
C. 10ms−110m{{s}^{-1}}
D. None of these.

Explanation

Solution

The relation between the applied force and the acceleration of the body due to that force is given as F=maF=ma. The direction in which the body accelerates is the same as the direction of the applied force.

Complete step by step answer:
From Newton's second law of motion, we understand that when a force is applied on the body of some mass, the body undergoes acceleration.The relation between the applied force and the acceleration of the body due to that force is given as F=maF=ma. The direction in which the body accelerates is the same as the direction of the applied force.

In the given question, it is said that a body is travelling along a straight line at a velocity of 5ms−15m{{s}^{-1}}. Then a force of 10N is applied on the body in the direction that is perpendicular to its initial line of motion.Suppose the body is moving along the x-axis initially. Then we can say that the force is applied along the y-axis.

Since the force is applied along the direction of the y-axis, the body will accelerate along the direction of the y-axis because the direction of acceleration is the same as that of the applied force. This means that the body accelerates along the direction of the y-axis only. Therefore, the acceleration of the body along the x-axis (i.e. the initial line of motion) is zero.

Hence, the correct option is B.

Note: From this question we can understand that the acceleration of a body does depend on the initial velocity of the body and the direction in which it is moving. The acceleration and its direction only depends on the applied force. In this case, the body will travel with a constant (equal to initial velocity) along the x-axis and will accelerate along the y-axis. If the force is constant, then it will trace a parabolic path.