Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
415 views
in Laws of motion by (15.2k points)
closed by

A smooth semicircular wire track of radius R is fixed in a vertical plane. One end of a massless spring of natural length 3R/4 is attached to the lowest point O of The wire track. A small ring of mass m which can slide on the track is attached to the other end of the spring. The ring is held stationary at point P such that the spring makes an angle with the vertical. The spring constant k = mg/R. 

Consider the instant when the ring is making an angle 60° with the vertical. The spring is released 

(a) Draw the free body diagram of the ring.

(b) Determine the tangential acceleration of the ring and the normal reaction?

2 Answers

+1 vote
by (39.0k points)
selected by
 
Best answer

(a) CP = CO = Radius of circle (R)

∴ ∠CPO = ∠POC = 60°

∴ ∠OCP is also 60°

Therefore, DOCP is an equilateral triangle.

Natural length of spring is 3R/4.

∴ Extension in the spring

\(x = R - \frac{3R}4 = \frac R4\)

⇒ Spring force,

\(F = kx = \left(\frac{mg}R\right)\left(\frac R4\right)= \frac{mg}4\)

The free body diagram of the ring will be as shown.

Here, F = kx = \(\frac {mg}4\)

and N = Normal reaction.

(b) Tangential acceleration aT : The ring will move forwards the x-axis just after the release. So net force along x-axis

Normal reaction N : Net force along y-axis on the ring just after the release will be zero.

+1 vote
by (15.7k points)

Answer is:

(a) mg/4, 

(b) atan = 5 \(\sqrt{3}\)g /8, N = 3mg / 8

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...