NEET
- Exam
- NEET
- Subject
- Physics
- Chapter
- Motion in Two Dimensions
NEET · Physics · Motion in Two Dimensions
A small block of mass m is tied to a string of length L and whirled...
A small block of mass is tied to a string of length and whirled in a circle on a smooth horizontal table. The string will break if the tension exceeds a certain maximum value. The maximum angular velocity with which the block can be whirled without breaking the string is . If the string is shortened to a length of , what will be the new maximum angular velocity before the string breaks?
Options
- A
- B
- C
- D
Correct answer
D.
Step-by-step solution
The tension in the string provides the necessary centripetal force for the circular motion of the block.
The maximum tension T_\max the string can withstand before breaking is given by:
T_\max = m L \omega_0^2
When the length of the string is halved to , the maximum tension the string can bear remains the same. Let the new maximum angular velocity be .
T_\max = m \left(\dfrac{L}{2}\right) (\omega')^2
Equating the two expressions for T_\max:
.
Answer:
The maximum tension T_\max the string can withstand before breaking is given by:
T_\max = m L \omega_0^2
When the length of the string is halved to , the maximum tension the string can bear remains the same. Let the new maximum angular velocity be .
T_\max = m \left(\dfrac{L}{2}\right) (\omega')^2
Equating the two expressions for T_\max:
.
Answer: