## OSCILLATIONS QUIZ 16

JEE Advanced Physics Syllabus can be referred by the IIT aspirants to get a detailed list of all topics that are important in cracking the entrance examination. JEE Advanced syllabus for Physics has been designed in such a way that it offers very practical and application-based learning to further make it easier for students to understand every concept or topic by correlating it with day-to-day experiences. In comparison to the other two subjects, the syllabus of JEE Advanced for physics is developed in such a way so as to test the deep understanding and application of concepts..

Q1. A uniform cylindrical metal rod A of length L and radius R is suspended at its mid-point from a rigid support through a strong metal wire of lengthl. The rod is given a small angular twist and released so that it oscillates to and fro about its mean position with a time period T1. Another body B of an irregular shape is suspended from the same rigid support using the same length of given suspension wire and its time period is found to be T2
The rotational inertia of metal rod about the wire as an axis is
•  a) (ML22)/12
•  b) (MR2)/2
•  c) M[L2/12+R2/2]
•  d) M[L2/12+R2/4]
Solution

Q2.A particle performs harmonic oscillation along the x-axis about the equilibrium positionx=0. The oscillation frequency isÏ‰=4.00 s(-1). At a certain moment of time the particle has a coordinate x0=25.0 cm and its velocity is equal to v(x0)=100 cms(-2) Find the amplitude of oscillation
•  13√3 cm
•  25√2 cm
•  27√5 cm
•  2√3 cm
Solution

Q3.  One end of an ideal spring is fixed to a wall at origin O and the axis of spring is parallel to the x-axis. A block of mass m=1 kg is attached to free end of the spring and it is performing SHM. Equation of position of the block in coordinate system shown in figure is x=10+3 sin (10 t), where t is in second and x in cm. Another block of mass M=3 kg, moving towards the origin with velocity 30 cm/s collides with the block performing SHM at t=0 and gets stuck to it
Solution

Q4. A block of mass m is connected to a spring of spring constant k and is at rest in equilibrium as shown. Now, the block is displaced by h below its equilibrium position and imparted a speed v_0 towards down as shown in figure. As a result of the jerk, the block executes simple harmonic motion about its equilibrium position. Based on this information, answer the following questions:
The amplitude of oscillation is
•  a) h
•  b) √((mv20)/k+h2 )
•  c) √(m/k v0+h)
•  d) None of these
Solution

Q5.A block of mass m is connected to a spring of spring constant k as shown in figure. The block is found at its equilibrium position at t=1 s and it has a velocity of +0.25 m/s at t=2 s. The time period of oscillation is 6 s
Based on the information, answer the following questions: The amplitude of oscillation is
•  3/2Ï€ m
•  3 m
•  1/Ï€ m
•  1.5 m
Solution

Q6. In a physical pendulum, the time period for small oscillation is given by, T=2Ï€√(I/Mgd) where I is the moment of inertia of the body about an axis passing through a pivoted point O and perpendicular to the plane of oscillation and d is the separation point between centre of gravity and the pivoted point. In the physical pendulum, a special point exists where if we concentrate the entire mass of body the resulting simple pendulum (w.r.t. pivot point O) will have the same time period as that of physical pendulum. This point is termed centre of oscillation. T=2Ï€√(I/Mgd)=2Ï€√(L/g) Moreover, this point possesses two other important remarkable properties: Property I: Time period of physical pendulum about the centre of oscillation (if it would be pivoted) is same as in the original case Property II: If an impulse is applied at the centre of oscillation in the plane of oscillation, the effect of this impulse at pivoted point is zero. Because of this property, this point is also known as the centre of percussion. From the given information answer the following questions: A uniform rod of mass M and length L is pivoted about point O as shown in figure. It is slightly rotated from its mean position so that it performs angular simple harmonic motion. For this physical pendulum, determine the time period of oscillation
•  2Ï€√(L/g)
•  Ï€√(7L/3g)
•  2Ï€√(2L/3g)
•  None of these

Solution

Q7.A block of mass m is suspended from one end of a light spring as shown. The origin O is considered at distance equal to natural length of the spring from the ceiling from the ceiling and vertical downward direction as positive y-axis. When the system is in equilibrium, a bullet of mass m/3 moving in vertical upward direction with velocity v_0 strikes the block and embeds into it. As a result, the block (with bullet embedded into it) moves up and starts oscillating. Based on the given information, answer the following question: Mark out the correct statement(s)
•  The block-bullet system performs SHM about y=mg/k
•  The block-bullet system performs oscillatory motion but not SHM about y=mg/k
•  The block –bullet system performs SHM about y=4mg/3k
•  The block-bullet system performs oscillatory motion but not SHM about y=4mg/3k
Solution

Q8.Two identical blocks A and B, each of mass m=3 kg, are connected with the help of an ideal spring and placed on a smooth horizontal surface as shown in figure. Another identical block C moving with velocity v_0=0.6 m/s collides with A and sticks to it, as a result, the motion of system takes place in some way
Based on this information, answer the following questions: After the collision of Cand A, the combined body and block B would
•  Oscillate about centre of mass of system and centre of mass is at rest
•  Oscillate about centre of mass of system and centre of mass is moving
•  Oscillate but about different locations other than the centre of mass
•  Not oscillate
Solution

Q9.A small of block of mass m is fixed at upper end a massive vertical spring of spring constant k=4mg/L and natural length ’10 L’. The lower end of spring is free and is at a height L from fixed horizontal floor as shown. The spring is initially unstressed and the spring-block system is released from rest in the shown position
At the instant the speed of block is maximum, the magnitude of force exerted by the spring on the block is
•  mg/2
•  mg
•  Zero
•  None of these
Solution

Q10. A 100 g block is connected to a horizontal massless spring of force constant 25.6 N/m. as shown in figure (a), the block is free to oscillate on a horizontal frictionless surface. The block is displaced 3 cm from the equilibrium position and, at t=0, it is released from from rest at x=0. It executes simple harmonic motion with the positive x-direction indicated in figure (a) The position-time (x-t) graph of motion of the block is as shown in figure
When the block is at position A on the graph, its
•  Position and velocity both are negative
•  Position is positive and velocity is negative
•  Position is negative and velocity is positive
•  Position and velocity both the positive
Solution

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