Oscillations-Quiz-6

OSCILLATIONS QUIZ 6

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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 spring is placed in vertical position by suspending it from a hook at its top. A similar hook on the bottom of the spring is at 11 cm above a table top. A mass of 75 g and of negligible size is then suspended from the bottom hook, which is measured to be 4.5 cm above the table top. The mass is then pulled down a distance of 4 cm and released. Find the approximate position of the bottom hook after 5 s? Take g=10 m/s ^2 and hook’s mass to be negligible

•  a) 5 cm above the table top
•  b) 4.5 cm above the table top
•  c) 9 cm above the table top
•  d) 0.5 cm above the table top

Solution

Q2.A vertical spring carries a 5 kg body and is hanging in equilibrium, an additional force is applied so that the spring is further stretched. When released from this position, it performs 50 complete oscillations in 25 s, with an amplitude of 5 cm. The additional force applied is

•  80 N
•  80π^2 N
•  4π^2 N
•  4 N

Solution

Q3.  A mass m attached to a spring of spring constant k is stretched a distance x_0 from its equilibrium position and released with no initial velocity. The maximum speed attained by mass in its subsequent motion and the time at which this speed would be attained are, respectively,

•  √(k/m) x₀,π√(m/k)
•  √(k/m) x₀/2, π/2 √(m/k)
•  √(k/m) x₀,π/2 √(m/k)
•  √(k/m) x₀/2, π √(m/k)

Solution

Q4. A particle performs simple harmonic motion about O with amplitude A and time period T. The magnitude of its acceleration at t=T/8 s after the particle reaches the extreme position would be

•  a) (4π² A)/√(2T² )
•  b) (4π² A)/(T² )
•  c) (2π² A)/√(2T² )
•  d) None of these

Solution

Q5.The K.E. and P.E. of a particle executing SHM with amplitude A will be equal when its displacement is:

•  A√2
•  A/2
•  A/√2
•  A√2/3

Solution
 

Q6. A particle executing harmonic motion is having velocities v_1 and v_2 at distances is x_1 and x_2 from the equilibrium position. The amplitude of the motion is

•  √((v_1^2 x_2-v_2^2 x_1)/(v_1^2+v_2^2 ))
•  √((v_1^2 〖x^2〗_1-v_2^2 〖x_2^2〗_ )/(v_1^2+v_2^2 ))
•  √((v_1^2 c_2^2-v_2^2 x_1^2)/(v_1^2-v_2^2 ))
•  √((v_1^2 x_2^2+v_2^2 x_1^2)/(v_1^2+v_2^2 ))

Solution

Q7.A thin uniform vertical rod of mass m and length l pivoted at point O is shown in figure. The combined stiffness to the springs is equal to k. The mass of the spring is negligible. The frequency of small oscillation is

•  √(3k/2m+g/l)
•  √(3k/2m+3g/l)
•  √(3k/m+3g/2l)
•  √(3k/m+2g/3l)

Solution

Q8.A uniform rod of length L and mass M is pivoted at the centre. Its two ends are attached to two springs of equal spring constant k. The springs are fixed to rigid supports as shown in the figure, and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle θ in one direction and released. The frequency of oscillation is

•  1/2π √(2k/M)
•  1/2π √(2k/M)
•  1/2π √(6k/M)
•  1/2π √(24k/M)

Solution

Q9.In problem 9, the acceleration of the particle is

•  (5√3 π)/2 m/s²
•  (5π²)/2 m/s²
•  (5√3 π)/4 m/s²
•  5√3π m/s²

Solution

Q10. A particle moves with a simple harmonic motion in a straight line. In the first second starting from rest it travels a distance a and in the next second it travels a distance b in the same direction. The amplitude of the motion is

•  (2a²)/(3b-a)
•  (3a²)/(3a-b)
•  (2a²)/(3a-b)
•  (3a²)/(3b-a)

Solution