Answer
Verified
91.2k+ views
Hint It is given in our question that a body is moving along a circular path of radius r. It is essential to understand that displacement is defined as the shortest distance travelled by the body undergoing this motion. Use this to find the value.
Complete Step By Step Solution
It is given that a body is moving along a circular path of given radius r. Hence , in one revolution it is said to complete a total distance r with an area of \[\pi {r^2}\]. In layman terms distance travelled by the object in a circular motion is said to be it’s circumference. So, when a body completes one full rotation , it is said to have covered a distance of \[2\pi r\].
Now displacement is defined as the shortest path the object takes to reach a point in the reference plane. Now, it is given that the body will complete half the revolution. In a circular motion, the shortest path a body can take from its starting point has to be in a straight line, covering its radius in full. Since the body is said to have travelled only half revolution, the total displacement from the starting point is twice the radius of the circle, \[2r\] and the distance travelled from the starting point is half the circumference of the circle which is \[\pi r\].
Therefore the displacement of the body in half revolution is \[2r\]. Hence , Option (b) is the right answer.
Note In a circular motion, we calculate velocity of the body quite differently from a linear velocity. At a given instance in its circular path, the body is said to make an angle with the reference plane. This angular change is called angular displacement and the velocity undergone by the body is called angular velocity.
Complete Step By Step Solution
It is given that a body is moving along a circular path of given radius r. Hence , in one revolution it is said to complete a total distance r with an area of \[\pi {r^2}\]. In layman terms distance travelled by the object in a circular motion is said to be it’s circumference. So, when a body completes one full rotation , it is said to have covered a distance of \[2\pi r\].
Now displacement is defined as the shortest path the object takes to reach a point in the reference plane. Now, it is given that the body will complete half the revolution. In a circular motion, the shortest path a body can take from its starting point has to be in a straight line, covering its radius in full. Since the body is said to have travelled only half revolution, the total displacement from the starting point is twice the radius of the circle, \[2r\] and the distance travelled from the starting point is half the circumference of the circle which is \[\pi r\].
Therefore the displacement of the body in half revolution is \[2r\]. Hence , Option (b) is the right answer.
Note In a circular motion, we calculate velocity of the body quite differently from a linear velocity. At a given instance in its circular path, the body is said to make an angle with the reference plane. This angular change is called angular displacement and the velocity undergone by the body is called angular velocity.
Recently Updated Pages
Name the scale on which the destructive energy of an class 11 physics JEE_Main
Write an article on the need and importance of sports class 10 english JEE_Main
Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main
Choose the one which best expresses the meaning of class 9 english JEE_Main
What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main
A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main
Other Pages
The vapour pressure of pure A is 10 torr and at the class 12 chemistry JEE_Main
Electric field due to uniformly charged sphere class 12 physics JEE_Main
3 mole of gas X and 2 moles of gas Y enters from the class 11 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main
Derive an expression for maximum speed of a car on class 11 physics JEE_Main
Velocity of car at t 0 is u moves with a constant acceleration class 11 physics JEE_Main