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 ra

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Solution

Q.
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 the tension in the spring is [2023]

1 0.50 N

2 0.75 N

3 1.5 N

4 0.25 N

Ans.
(2)

Let extension in length of spring be $x$ .

Radius of circle, $r = 0.2 + x$

$k x = m ω^{2} r$

$7.5 x = (\frac{1}{10}) {(5)}^{2} (0.2 + x)$

$\Rightarrow \frac{15}{2} x = \frac{5}{2} (x + \frac{1}{5})$

$\Rightarrow x = \frac{1}{10}$

$∴$ $Tension in spring = k x = 7.5 \times \frac{1}{10} = 0.75 N$

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