NEETPhysicsExperimental Physics
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): A coin of diameter d placed at a distance of 57.3 d from the eye subtends an angle of approximately 1 radian . Reason (R): 1 radian is approximately equal to 57.3^ . In the light of the above statements, choose the most appropriate answer from the options given below:
Options
- ABoth (A) and (R) are true and (R) is the correct explanation of (A)
- BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
- C(A) is true but (R) is false
- D(A) is false but (R) is true
Correct answer
D. (A) is false but (R) is true
Step-by-step solution
The angle subtended by the coin at the eye is given by the small angle approximation = arc radius d 57.3 d = 1 57.3 rad . We know that rad = 180^ , which gives 1 rad = 180 57.3^ . Therefore, the angle subtended is = ( 1 57.3 ) 57.3^ = 1^ . Thus, the coin subtends an angle of approximately 1^ , not 1 radian . Hence, the Assertion (A) is false. The Reason (R) correctly states the approximate value of 1 radian in degrees, so it is true. Answer: (A) is false but (R) is true