Question

An object of mass 0.5 kg is tied to a string and revolved in a horizontal circle of radius 1m. If the breaking tension of the string is 50 N, what is the maximum speed the object can have?​

Answer 1

GIVEN :

• Mass, m = 0.5 kg.
• Radius of a circle, r = 1 m.
• Breaking tension of the spring, T = 50 N.

TO FIND :

• Maximum speed of the object, $\sf V_{max}$ = ?

FORMULA USED :

• $\sf T \: = \: \dfrac{mv^2_{max}}{radius}$
• $\sf V_{max} \: = \: \sqrt{\dfrac {Tr}{m}}$

Here,

m = mass of an object.

T = Tension of the spring.

r = radius of the circle.

$\sf V_{max}$ = maximum velocity.

SOLUTION :

$\implies \sf T \: = \: \dfrac{mv^2_{max}}{radius}$

$\implies \sf V_{max} \: = \: \sqrt{\dfrac {Tr}{m}}$

$\implies \sf V_{max} \: = \: \sqrt{\dfrac {50 \ \times \ 1}{0.5}}$

$\implies \sf V_{max} \ = \ \sqrt{100}$

$\implies \sf V_{max} \ = \ 10 \: m/s^{2}$

•°• Therefore, the maximum speed the object have is $10 \: m/s^{2}$