Home
Class 11
PHYSICS
One end of an ideal spring is fixed to a...

One end of an ideal spring is fixed to a wall at origin `O` and axis of spring is parallel to x-axis. A block of mass `m = 1kg` is attached to free end of the spring and it is performing SHM. Equation of position of the block in co-ordinate system shown in figure is `x = 10 + 3 sin (10t)`. Here, t is in second and `x` in `cm`. Another block of mass `M = 3kg`, moving towards the origin with velocity `30 cm//s` collides with the block performing SHM at `t = 0` and gets stuck to it. Calculate

(a) new amplitude of oscillations,
(b) neweqution for position of the combined body,
( c) loss of energy during collision. Neglect friction.

A

`20 (rad)/(s)`

B

`5(rad)/(s)`

C

`100(rad)/(s)`

D

`50(rad)/(s)`

Text Solution

Verified by Experts

The correct Answer is:
B
`omega=sqrt((K)/(m))`, `K=omega^2m=(10)^2=100(N)/(m)`
Angular frequency of oscillatino of combined body is
`omega'=sqrt((K)/(m+M))=sqrt((100)/(4))=5(rad)/(s)`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS ENGLISH|Exercise Integer|10 Videos

  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS ENGLISH|Exercise Subjective type|2 Videos

  • LINEAR AND ANGULAR SIMPLE HARMONIC MOTION

    CENGAGE PHYSICS ENGLISH|Exercise Assertion Reasoning|6 Videos

  • KINETIC THEORY OF GASES AND FIRST LAW OF THERMODYNAMICS

    CENGAGE PHYSICS ENGLISH|Exercise Interger|11 Videos

  • MISCELLANEOUS KINEMATICS

    CENGAGE PHYSICS ENGLISH|Exercise Interger type|3 Videos

Similar Questions

Explore conceptually related problems

A spring has natural length 40 cm and spring constant 500 N//m . A block of mass 1 kg is attached at one end of the spring and other end of the spring is attached to a ceiling. The block is relesed from the position, where the spring has length 45 cm .

a block of mass 0.1 kg attached to a spring of spring constant 400 N/m pulled horizontally from x=0 to x_1 =10 mm. Find the work done by the spring force

Two identical springs of spring constant k are attached to a block of mass m and to fixed supports as shown in the figure. The time period of oscillation is

A block of mass 0.1 kg attached to a spring of spring constant 400 N/m is putted rightward from x_(0)=0 to x_(1)=15 mm. Find the work done by spring force.

An ideal spring with spring constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

An ideal spring with spring constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

A block of mass m is dropped onto a spring of constant k from a height h . The second end of the spring is attached to a second block of mass M as shown in figure. Find the minimum value of h so that the block M bounces off the ground. If the block of mass m sticks to the spring immediately after it comes into contact with it.

Tow identical springs of spring constant k are attached to a block of mass m and to fixed supports as shown in figure. When the mass is displaced from equilibrum position by a distance x towards right, find the restoring force.

One end of a light spring of spring constant k is fixed to a wall and the other end is tied to a block placed on a smooth horizontal surface. In a displacement, the work by the spring is 1/2kx^2 . The possible cases are

A block of mass m is attached to a cart of mass 4m through spring of spring constant k as shown in the figure. Friction is absent everywhere. The time period of oscillations of the system, when spring is compressed and then released, is

Home
Profile