MHT CET202312 May 2023Morning ShiftPhysicsLaws of MotionActual
Four massless springs whose force constants are 2 ~K , 2 ~K , ~K and 2 ~K respectively are attached to a mass M kept on a frictionless plane as shown in figure, If mass M is displaced in horizontal direction then frequency of oscillating system is
Options
- A1 2 K 4 M
- B1 2 4 ~K M
- C1 2 K 7 M
- D1 2 7 ~K M
Correct answer
B. 1 2 4 ~K M
Step-by-step solution
On the right hand side of the block, springs are connected in parallel Their effective spring constant is given by aligned & K ₁= K +2 ~K & ~K ₁=3 ~K aligned On the left hand side of the block, springs are connected in series. Their effective spring constant is given by, aligned & 1 ~K ₂ = 1 2 ~K + 1 2 ~K K ₂ & = K aligned Effective spring constant of the system is given by, aligned & K _ E =3 ~K + K =4 ~K & = K _ E M = 4 ~K M f & = 2 = 1 2 4 ~K M aligned