Bissoy.com
Doctors Medicines MCQs Q&A

A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has a force constant value k. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be:

A block of mass M is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has a force constant value k. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be: Correct Answer 2 Mg/k

CONCEPT:

  • Potential energy(P.E):  It is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
    • For example, raised weight, water that is behind a dam, a car that is parked at the top of a hill, a snowpack (potential avalanche).

Formula :

Potential energy gained(P.E)G = 1/2 Kx2

Potential energy lost(P.E)L = mgh

where, k = spring constant, x = spring displacement, m = mass (kg), h = height of spring (m).

  • Conservation of energy: It states that energy can neither be created nor be destroyed but it can be transformed from one form to another.
    • For example, compressed spring is released then P.E gained is equal to P.E lost by spring.

EXPLANATION:

From the above discussion,

Applying conservation of energy

Potential energy gained = Potential energy lost

(1/2) kx2 = m g x

x = 2mg/k

The correct option is 1.

Related Questions

A spring mass system is on a horizontal plane. Spring constant is 2N/m & mass of block is 2kg. The spring is compressed by 10cm and released. A small ball is released from a height of 2m above the block on the horizontal plane. At what time should the ball be left if the block is released from the extreme position at t=0, given that the ball has to fall on the block when the speed of block is maximum?
A tank has an optional adjustable outlet pipe that can be attached to the tank at any height we want. This outlet pipe drains water from the tank at a constant rate, while the tank is being filled using another inlet pipe at a constant rate. If the outlet, pipe is attached at half the height of the tank, the tank, which is initially empty gets filled in 18 hours. If the outlet pipe is attached at height equal to two third height of the tank, the tank, which is initially empty, is filled in 16 hours. In how many hours will the tank, which is initially empty, be completely filled if the outlet pipe is not attached to the tank?
Five movies A, B, C, D, and E are to be released on five different days from Monday to Friday, one movie per day, by keeping the following rules in mind:- [1] Movie D cannot be released on Monday. [2] If movie A is released on Monday then movie D will be released on Friday. [3] If movie D is released on Tuesday then movie B will be released on Monday. [4 ] Movie C is released on the next day of release of movie E. If movie B was released on Tuesday, then which movie was released on Monday?
Natural length of spring is 60 cm and its spring constant is 4000 N/m. A mass of 20 kg is hung from it. The extension produced in the spring (take g=9.8m/s2) is?
The notification for six different posts - Clerk, PRO, Lecturer, Accountant, Watchman and Principal- are to be released on consecutive Fridays. The schedule of the releasing is to be in accordance with the following conditions: (i) Clerk post must be released a week before the Watchman post. (ii) Lecturer post must not be released immediately after the first release. (iii) PRO post must be released on the Friday following the Friday on which the Principal post is released. (iv) Accountant post must be released on the fifth Friday and should not be immediately preceded by the PRO post. (v) The Watchman post must not be released last. Which of the following notifications will be released immediately after the PRO post?
A spring block system is on a horizontal surface. The block is compressed by 10cm. What should be the coefficient of friction between the block and ground such that the block comes to a stop at the mean position? Mass of block = 0.5kg & spring constant = 3N/m.
A block whose mass is 650 gm is fastened to aspring constant K equals 65 N/m whose other end is fixed. The block is pulled a distance x = 11 cm from its equilibrium position at x = 0 on a smooth surface, and released from rest at t = 0. The maximum speed ‘S’ of the oscillating block is
Profit on selling 10 ceiling fans equal selling price of 3 coolers. While loss on selling 10 coolers equal selling price of 4 ceiling fans. Also profit percentage equals to the loss percentage and cost of a ceiling fan is half the cost of a cooler. What is the ratio of selling price of ceiling fan to the selling price of a cooler?
A spring of spring constant 5×103N/m is stretched initially by 5cm from the unstretched position. Then the work done to stretch is further by another 5cm is?
A load of 100N falls through a height of 2cm onto a collar rigidly attached to the lower end of a vertical bar 1.5m long and of 105cm2 cross- sectional area. The upper end of the vertical bar is fixed. What is the maximum instantaneous stress induced in the vertical bar if E = 200GPa?