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Physics Question on Uniform Circular Motion

A small block of mass 100 g is tied to a spring of spring constant 7.5 N/m and length 20 cm. The other end of spring is fixed at a particular point A. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity 5 rad/s about point A, then tension in the spring is-

A

0.75N

B

1.5N

C

0.25N

D

0.50N

Answer

0.75N

Explanation

Solution

A small block of mass 100 g is tied to a spring of spring
š‘˜š‘„ = š‘ššœ”^2 š‘Ÿ
āŸ¹ š‘˜š‘„ = 0.1 Ɨ 25 Ɨ (0.2 + š‘„)
āŸ¹ 7.5š‘„ = 2.5(0.2 + š‘„) āŸ¹ 3š‘„ = 0.2 + š‘„
āŸ¹ 2š‘„ = 0.2 āŸ¹ š‘„ = 0.1š‘š
Now, tension in the spring = š‘˜š‘„ = 7.5 Ɨ 0.1 š‘ = 0.75 N