A wedge of mass M fitted with a spring of stiffness 'k' is kept on a smooth horizontal surface. A rod of mass m is kept on the wedge as shown in the figure. System is in equilibrium. Assuming that all surfaces are smooth, the potential energy stored on the spring is:

A)\[\frac{mg^2tan^2\theta}{2k}\] B)\[\frac{m^2gtan^2\theta}{2k}\] C)\[\frac{m^2g^2tan^2\theta}{2k}\] D)\[\frac{m^2g^2tan^2\theta}{k}\]

## Comments

Sort by:

TopNewestMake free body diagram of forces on both the blocks one by one. For wedge of mass M the forces acting along the floor are N sinθ (normal reaction from block of mass m) and kx. Next, make free body diagram of block of mass m. Forces acting on it perpendicular to the floor are N cosθ and mg. Solving these equations

Nsinθ = kx,

Ncosθ = mg,

We get the value of x, hence value of potential energy can be evaluated. – Lokesh Sharma · 4 years, 4 months ago

Log in to reply

c – Vijay Sakhamudi · 4 years, 4 months ago

Log in to reply

– Shubham Srivastava · 4 years, 4 months ago

Solution????Log in to reply

Start with determining the state of spring at equilibrium. Should it be compressed or stretched to keep the system at equilibrium? – Pranav Arora · 4 years, 4 months ago

Log in to reply

make forces acting on M, weight of m & a force F which is acts opposite to spring force to keep system is in equilibrium. then \Tan\theta\ = F\mg. from this find out F and substituted in P.E = F*2\ 2K get the ans... (C) is correct – Srinivas Santoshi · 4 years, 3 months ago

Log in to reply

My attitude towards the problem is this: The weight, mg, of the rod will have 2 components- mgsin0 and mgcos0. The component, mgcos0, can be again resolved into two vectors having a horizontal component, mgcos0sin0. For equilibrium, the spring force should be equal to horizontal force. Therefore, mgcos0sin0= kx. We can now substitute value of x from this equation in the equation for spring potential energy, i.e., 0.5kx^2. – Shubham Srivastava · 4 years, 4 months ago

Log in to reply

– Lokesh Sharma · 4 years, 4 months ago

I fear your reasoning is not accurate. You are making components of components. This is probably wrong way and you will get the wrong answer I think.Log in to reply

so,

mgcos0sin0 = kx

x=(mgcos0sin0)/k

the potential energy stored in spring = 1/2(k . x^2)..

solvong further will give the answer... So the explanation of Shubham S is accurate.... – Samarth M.O. · 4 years, 2 months ago

Log in to reply

BY DIMENSIONAL ANALYSIS IT CAN ONLY BE C OR D MOSTLY C – Vasanth Balakrishnan · 4 years, 4 months ago

Log in to reply

– Pranav Arora · 4 years, 4 months ago

Mind keeping Caps Lock off. :PLog in to reply

– Suresh Muthuraman · 4 years, 3 months ago

how can u say it is mostly c)?Log in to reply