A body is moving with constant speed, in a circle of radius $10 m$ .The body completes one revolution in 4 s .At the end of 3 rd second, the displacement of body (in mi) from its starting point is :
A body is moving with constant speed, in a circle of radius $10 m$ .The body completes one revolution in 4 s .At the end of 3 rd second, the displacement of body (in mi) from its starting point is :
Show Hint
- $15 \pi$
- $10 \sqrt{2}$
- 30
- $5 \pi$
The Correct Option is B
Approach Solution - 1
From the given figure above , we get
Speed, v = constant
Radius, R = 10 m
T = Time period = 4s
At the end of 3rd second, particle will be at D (Starts from A)
\(\therefore\) displacement S = \(\sqrt2R\)
\(=\sqrt2\times10\)
\(=10\sqrt2\)
So, the correect answer is (B) : $10 \sqrt{2}$
Approach Solution -2
Given: The circle of the radius (R) = 10m,
Speed is constant,
Total time given = 4s
Displacement is the shortest distance between the initial and the final position.
From the above diagram it is clear that the initial position of the body is at A and the final position is D.
Total time of 4 seconds is evenly distributed for each segment of the orbit:
- It takes 1 second to travel from point A to point B
- Similarly, it takes 1 second from point B to point C
- Another 1 second is required to travel from point C to point D
- Finally, 1 more second from D to A to complete one revolution.
At the end of the 3rd second, the particle will be at D (when Starts from A).
As from the figure, it is clear AOD is right angled triangle, applying Pythagoras theorem, Displacement = S
\(S=\sqrt{AQ^2+OD^2}\)
\(S=\sqrt{R^2+R^2}\)
\(S=R\sqrt{2}\)
\(S=10\sqrt{2}\)
Therefore, At the end of 3 rd second, the displacement of body (in mi) from its starting point is \(10\sqrt{2}.\)
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
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- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.