A simple pendulum of length L is suspended from the ceiling of a cart which is sliding without friction on an inclined plane of inclination θ. The time period of the pendulum is

1.  T = 2πLg

2.  T = 2πLg cosθ

3.  T = 2πLg sinθ

4.  T = 2πLg tanθ

Subtopic:  Simple Harmonic Motion | Angular SHM |
 69%
From NCERT
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A body is placed on a horizontal platform that is undergoing vertical SHM. If the amplitude of oscillation is 40 cm, then the least period of oscillation for which an object placed over the platform is not detached from it is:

1.  1.256 s

2.  12.56 s

3.  0.1256 s

4.  125.6 s

Subtopic:  Simple Harmonic Motion |
 61%
From NCERT
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If a pendulum giving correct time on the ground at a certain place is moved to the top of a tower 320 m high, then the loss in time (in seconds) measured by the pendulum clock in one week is:

1.  15.12

2.  7.72

3.  3.78

4.  30.24

Subtopic:  Angular SHM |
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Instantaneous acceleration (in ms-2) of a particle executing S.H.M. is given by a = -π4sinπ4t - π6.  The maximum speed of the particle will occur first time at

1.  1.75 s

2.  1.4 s

3.  1.2 s

4.  0.67 s

Subtopic:  Simple Harmonic Motion |
 72%
From NCERT
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A particle moves according to the equation x = Acosπ2tDistance covered by it in the time interval of t =0 to t =3 s is: (symbols have their usual meanings) 

1.  A

2.  4A

3.  3A

4.  2A

Subtopic:  Simple Harmonic Motion |
 60%
From NCERT
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Two simple pendulums of length 1 m and 16 m are in the same phase at the mean position at any instant. If T is the time period of the smaller pendulum, then the minimum time after which they will again be in the same phase will be:

1.  3T2

2.  3T4

3.  2T3

4.  4T3

Subtopic:  Angular SHM |
From NCERT
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A body of mass m hanging with the help of three springs, each of spring constant k as shown. If the mass is slightly displaced and released, then the system will oscillate with the time period

                     

1.  2πm3k

2.  2π2m3k

3.  2π3m2k

4.  2π3mk

Subtopic:  Combination of Springs |
 82%
From NCERT
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A block of mass m attached to a spring of constant k oscillates on a smooth surface. The other end of the spring is fixed to a wall. When spring is at its natural length, the speed of the block is v. Displacement of the block from its mean position before coming to instantaneous rest is:

1.  mvk

2.  vmk

3.  mvk

4.  1kmv

Subtopic:  Energy of SHM |
 81%
From NCERT
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A particle under SHM has a maximum speed of 30 cm/s and a maximum acceleration of 60 cm/s? The time period of oscillation (in second) is

1.  π2

2.  2π

3.  π

4.  4π

Subtopic:  Simple Harmonic Motion |
 83%
From NCERT
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The x-t graph of a particle undergoing SHM is shown below. The acceleration of the particle at t = 43 is:

                      

1.  332π3 cm/s2

2.  -π232 cm/s2

3.  π232 cm/s2

4.  -332π2 cm/s2

Subtopic:  Simple Harmonic Motion |
 68%
From NCERT
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