Home
Class 12
PHYSICS
A ring of mass m can slide over a smooth...

A ring of mass m can slide over a smooth vertical rod. The ring is connected to a spring of force constant `K=(4mg)/R` where 2R is the natural length of the spring. The other end spring is fixed to the ground at a horizontal distance 2R from the base of the rod. the mass is released at a height of 1.5 R from ground.

A

`(mgR)/(2)`

B

`(3mgR)/(2)`

C

`(3mgR)/(5)`

D

`mgR`

Text Solution

Verified by Experts

The correct Answer is:
A
`AC=sqrt((2R)^2+((3)/(2)R)^2)=(5)/(2)R`
Extension in length of spring `(x)=(5)/(2)R=2R=(R )/(2)`
Work done by spring `=(1)/(2)kx^2`
`=(1)/(2)((4mg)/(R ))((R^2)/(4))=(mgR)/(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

A ring of mass m can slide over a smooth vertical rod as shown in figure. The ring is connected to a spring of force constant k = 4 mg//R , where 2R is the natural length of the spring . The other end of spring is fixed to the ground at a horizontal distance 2R from base of the rod . If the mass is released at a height 1.5 J then the velocity of the ring as it reaches the ground is

A ring of mass m=10kg can slide through a vertical rod with friction. It is connected with a spring of force constant k=100Nm^-1 . The relaxed length of spring is 4m . The ring is displaced 3m as shown in the figure and released. Find velocity of ring when spring becomes horizontal.

A bead of mass m can slide without friction along a vertical ring of radius R. One end of a spring of force constant k=(3mg)/(R ) is connected to the bead and the other end is fixed at the centre of the ring. Initially, the bead is at the point A and due to a small push it starts sliding down the ring. If the bead momentarily loses contact with the ring at the instant when the spring makes an angle 60^(@) with the vertical, then the natural length of the spring is

A bead of mass m can slide without friction on a fixed circular horizontal ring of radius 3R having a centre at the point C. The bead is attached to one of the ends of spring of spring constant k. Natural length of spring is R and the other end of the spring is R and the other end of the spring is fixed at point O as shown in the figure. If the bead is released from position A, then the kinetic energy of the bead when it reaches point B is

A ring of mass m is attached to a horizontal spring of spring constant k and natural length l_0 . The other end of the spring is fixed and the ring can slide on a horizontal rod as shown. Now the ring is shifted to position B and released Find the speed of the ring when the spring attains its natural length.

A ring of mass m can slide on the vertical smooth rod. Ring is connected by block with string as shown in figure. Pulley is of mass-less and smooth the system is released from reast. Initial tension in string is

A ring of mass m can freely slide on a smooth vertical rod. The ring is symmetrically attached with two springs, as shown, each of stiffness k . Ring is displaced such that each spring makes an angle theta with the horizontal. If the ring is slightly displaced vertically, then time period is.......

A small block of mass m, can move without friction on the outside of a fixed vertical circular track of radiusR. The block is attached to a spring of natural length R//2 and spring constant K. The other end of spring is connected to a point at height R//2 directly above the centre of track. If the block is released from rest when the spring is in horizontal state (see figure) then at that moment,

A light rod AB is fitted with a small sleeve of mass m which can slide smoothly over it. The sleeve is connected to the two ends of the rod using two springs of force constant 2k and k (see fig). The ends of the springs at A and B are fixed and the other ends (connected to sleeve) can move along with the sleeve. The natural length of spring connected to A is l_(0) . Now the rod is rotated with angular velocity w about an axis passing through end A that is perpendicular to the rod. Take (k)/(momega^(2)) = eta and express the change in length of each spring (in equilibrium position of the sleeve relative to the rod) in terms of l_(0) and eta .

A block of mass M is tied to a spring of force constant k and placed on a smooth horizontal surface. The natural length of the spring is L. P is a point on the spring at a distance (L)/(4) from its fixed end. The block is set in oscillations with amplitude A. Find the maximum speed of point P on the spring.