A 2 kg block is gently pushed from rest at A and it slides down along the fixed smooth circular surface as shown in figure. If the attached spring has a force constant k = 20 N / m . What is unstretch

Question

A 2 kg block is gently pushed from rest at A and it slides down along the fixed smooth circular surface as shown in figure. If the attached spring has a force constant $k = 20 N / m$ . What is unstretched length of spring (in m ) so that it does not allow the block to leave the surface until angle with the vertical is $θ = 6 0^{\circ}$ ?

TestHub · Accepted Answer

2 1 ​ m v 2 = mgR ( 1 − cos θ ) ⇒ v = 2 g R × 2 1 ​ ​ = g R ​ Applying NLM along the radial direction: mg cos θ + kx = R mv 2 ​ ⇒ x = 2 1 ​ m Extension in spring = 0.5 m ⇒ Natural length = ( R − x ) = 1 m

Physics - Circular Motion Question with Solution | TestHub

Doubts & Discussion

JEE Advanced 2027 (Class 12+)