a body moves in a circular path find distance and displacement from :- (1) A to B (2) A to b to c (3) A to B to C to D ( 4 ) A to B to C to D to A
Answers
Answer:
1) distance - 11cm , displacement - 7root2 (2) distance - 22cm , displcement - 14cm (3) distance - 33cm , displacement - 7root2 (4) distance - 44cm , displacement - 0
Explanation:
(1) from A to B,
distance = 7.86 units
displacement = 5√2 units
(2) from A to B to C,
distance = 15.71 units
displacement = 10 units
(3) from A to B to C to D,
distance = 23.57 units
displacement = - 5√2 units
(4) from A to B to C to D to A,
distance = 31.43 units
displacement = 0
Given: a body moves in a circular path and the circular part is divided into four quarters A, B, C, and D.
To Find: distance and displacement
Solution:
1. The question is missing the value of the radius, so let's take the radius to be 5 units.
2. Distance is the path taken on the circumference only. Since it is a scalar so distance has to be always positive or zero.
3. Displacement is the shortest path available and it may or may not be through the circumference of the circular path. Also since displacement is a vector and hence it can be positive, negative, or zero.
(1) For the first part, from A to B we can see that it is a quarter of a circular path,
So, the distance of quarter = 1/4 × 2πr
= 1/4 × 2 × 22/7 ×5
= 7.86 units
and displacement is the shortest path available which is the hypotenuse, so using the Pythagorean formula,
the displacement = √( 5^2 + 5^2)
= 5√2 units
(2) For the second part, from A to B to C, we can see that it is half of a circular path,
So, the distance = 1/2 × 2πr
= 1/2 × 2 × 22/7 ×5
= 15.71 units
and displacement is equal to the diameter of the circular path,
the displacement = 2 × r
= 2× 5
= 10 units
(3) For the third part, from A to B to C to D, we can see that it is the 3/4th quarter of a circular path,
So, the distance = 3/4 × 2πr
= 3/4 × 2 × 22/7 ×5
= 23.57 units
and displacement is the shortest path available in the negative direction, which is the hypotenuse, so using the Pythagorean formula,
the displacement = √( 5^2 + 5^2)
= - 5√2 units [ negative direction]
(4) For the fourth part, from A to B to C to D to A, we can see that it is the entire circumference of a circular path,
So, the distance = 2πr
= 2 × 22/7 ×5
= 31.43 units
And since the path starts and ends at the same point (A), so displacement equals to zero.
the displacement = 0
Hence compiling all the answers,
(1) from A to B,
distance = 7.86 units
displacement = 5√2 units
(2) from A to B to C,
distance = 15.71 units
displacement = 10 units
(3) from A to B to C to D,
distance = 23.57 units
displacement = - 5√2 units
(4) from A to B to C to D to A,
distance = 31.43 units
displacement = 0
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