NEET
- Exam
- NEET
- Subject
- Physics
- Chapter
- Mechanical Properties of Fluids
NEET · Physics · Mechanical Properties of Fluids
Given below are two statements: one is labelled as Assertion (A)...
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): For a solid sphere of a given material falling through a viscous liquid, the viscous force acting on it at terminal velocity is directly proportional to the cube of its radius.
Reason (R): The terminal velocity of a solid sphere falling through a viscous liquid is directly proportional to the cube of its radius.
In the light of the above statements, choose the correct answer from the options given below:
Assertion (A): For a solid sphere of a given material falling through a viscous liquid, the viscous force acting on it at terminal velocity is directly proportional to the cube of its radius.
Reason (R): The terminal velocity of a solid sphere falling through a viscous liquid is directly proportional to the cube of its radius.
In the light of the above statements, choose the correct 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
C. (A) is true but (R) is false
Step-by-step solution
At terminal velocity, the net force on the sphere is zero. The downward weight is balanced by the upward buoyant force and viscous force.
Thus, the viscous force at terminal velocity is directly proportional to . Therefore, Assertion (A) is true.
According to Stokes' law, the terminal velocity of a sphere is given by:
This shows that terminal velocity is directly proportional to the square of the radius (), not the cube. Therefore, Reason (R) is false.
Answer: (A) is true but (R) is false
Thus, the viscous force at terminal velocity is directly proportional to . Therefore, Assertion (A) is true.
According to Stokes' law, the terminal velocity of a sphere is given by:
This shows that terminal velocity is directly proportional to the square of the radius (), not the cube. Therefore, Reason (R) is false.
Answer: (A) is true but (R) is false