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Oscillations · Question 42

AIPMT 2007MCQMedium📈 Topic in 12% papers+4−1
1

A mass of 2.0 kg is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is 200 N/m. What should be the minimum amplitude of the motion so that the mass gets detached from the pan (take g = 10 m/s2). [figure]

  1. 10.0 cm
  2. any value less than 12.0 cm
  3. 4.0 cm
  4. 8.0 cm

Answer

(1) 10.0 cm

Solution

The mass leaves the pan when the normal reaction becomes zero, i.e., at the highest point the downward acceleration of the pan equals g.

Maximum acceleration in SHM = 2 A = kmA

kmA = g

A = mgk = 2.0 10200

= 0.1 m = 10.0 cm

Answer: (1)

AIPMT 2007

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2

The particle executing simple harmonic motion has a kinetic energy K0 2 t. The maximum values of the potential energy and the total energy are respectively

  1. K0/2 and K0
  2. K0 and 2K0
  3. K0 and K0
  4. 0 and 2K0
AIPMT 2007
3

The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is

  2. 0.707
  3. zero
  4. 0.5
AIPMT 2007
4

A rectangular block of mass m and area of cross-section A floats in a liquid of density . If it is given a small vertical displacement from equilibrium it undergoes oscillation with a time period T, then

  1. T 1 m
  2. T
  3. T 1 A
  4. T 1
AIPMT 2006
5

The circular motion of a particle with constant speed is

  1. periodic but not simple harmonic
  2. simple harmonic but not periodic
  3. periodic and simple harmonic
  4. neither periodic nor simple harmonic
AIPMT 2005
6

A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm/s. The frequency of its oscillation is

  1. 4 Hz
  2. 3 Hz
  3. 2 Hz
  4. 1 Hz
AIPMT 2004
7

Two springs of spring constants k1 and k2 are joined in series. The effective spring constant of the combination is given by

  1. k1k2
  2. (k1 + k2)/2
  3. k1 + k2
  4. k1k2/(k1 + k2)
AIPMT 2004
8

Which one of the following statements is true for the speed v and the acceleration a of a particle executing simple harmonic motion?

  1. When v is maximum, a is maximum
  2. Value of a is zero, whatever may be the value of v.
  3. When v is zero, a is zero
  4. When v is maximum, a is zero.
AIPMT 2003
9

The potential energy of a simple harmonic oscillator when the particle is half way to its end point is

  1. 23E
  2. 18E
  3. 14E
  4. 12E
AIPMT 2003
10

A particle of mass m oscillates with simple harmonic motion between points x1 and x2, the equilibrium position being O. Its potential energy is plotted. It will be as given below in the graph

  1. [figure]
  2. [figure]
  3. [figure]
  4. [figure]
AIPMT 2003
11

The time period of mass suspended from a spring is T. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be

  1. T/4
  2. T
  3. T/2
  4. 2T
AIPMT 2003

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