Oscillations-Quiz-8

OSCILLATIONS QUIZ 8

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Q1. Two springs are made to oscillate simple harmonically due to the same mass individually. The time periods obtained are T₁ and T₂. If both the springs are connected in series and then made to oscillate by the same mass, the resulting time period will be

•  a) T₁+T₂
•  b) (T₁ T₂)/(T₁+T₂ )
•  c) √(T₁²+T₂² )
•  d) (T₁+T)/2

Solution

Q2.A hallow sphere is filled with water. It is hung by a long thread to make it a simple pendulum. As the water flows out of a hole at the bottom of the sphere, the frequency of oscillation will

•  Go on increasing
•  Go on decreasing
•  First increases and then decreases
•  First decreases and then increases

Solution

Q3.  A particle is performing SHM. Its kinetic energy K varies with time t as shown in the figure. Then

Period of oscillations of the particle is equal to T

•  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
•  Excess potential energy U of the particle varies with time t as shown in figure (a)
•  Excess potential energy U of the particle varies with time t as shown in figure (a)
•  None of these

Solution

Q4. A block (B) is attached to two unstretched springs S_1 and S_2 with spring constants k and 4 k, respectively (see figure I). The other ends are attached to identical supports M_1 and M_2 not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block B is displaced towards wall 1 by a small distance x (figure II) and released. The block returns and moves a maximum distance y towards wall 2. Displacements x and y are measured with respect to the equilibrium position of the block B. The ratio y/x is

•  a) 4
•  b) 2
•  c) 1/2
•  d) 1/4

Solution

Q5.A body of mass m is released from a height h to a scale pan hung from a spring. The spring constant of the spring is k, the mass of the scale pan is negligible and the body does not bounce relative to the pan; then the amplitude of vibration is

•  mg/k √(1-2hk/mg)
•  mg/k
•  mg/k+mg/k √(1+2hk/mg)
•  mg/k-mg/k √(1-2hk/mg)

Solution
 

Q6. A uniform semicircular ring having mass m and radius r is hanging at one of its ends freely as shown in figure. The ring is slightly disturbed so that it oscillates in its own plane. The time period of oscillation of the ring is

•  2π√(r/g(1+1⁄π^2 ) )
•  2π√(r/(g(1-4⁄π^2 )^(1⁄2) ))
•  2π√(r/(g(1-2⁄π^2 )^(1⁄2) ))
•  2π√(2r/(g(1+4⁄π^ )^(1⁄2) ))

Solution

Q7.Frequency of a particle executing SHM is 10 Hz. The particle is suspended from a vertical spring. At the height point of its oscillation the spring is unstretched. Maximum speed of the particle is (g=10 m/s²)

•  2π m/s
•  π m/s
•  1/π m/s
•  1/2π m/s

Solution

Q8.A small block is connected to one end of a massless spring of un-stretched length 4.9m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2m and released from rest at t=0. It then executes simple harmonic motion with angular frequency ω=π/3 rad/s. Simultaneously at t=0, a small pebble is projected with speed v from point P is at angle of 45° as shown in the figure. Point P is at a horizontal distance of 10 m from O. If the pebble hits the block at t=1s, the value of v is (take g=10m/s2)

•  √50 m/s
•  √51 m/s
•  √52 m/s
•  √53 m/s

Solution

Q9.Two spring, each of unstretched length 20 cm but having different spring constants k_1=1000 N/m and k_2=3000 N/m, are attached to two opposite faces of a small block of mass m=100 g kept on a smooth horizontal surface as shown in the figure

The outer ends of the two springs are now attached to two attached to two pins P_1 and P_2 whose locations are shown in the figure. As a result of this, the block acquires a new equilibrium position. The block has been displaced by small amount from its equilibrium position and released to perform simple harmonic motion; then

•  New equilibrium position is at 35 cm from P₁ and time period of simple harmonic motion is π/100 s
•  New equilibrium position is at 20 cm from P₁ and time period of simple harmonic motion is π/100 s
•  New equilibrium position is at 35 cm from P₁ and time period of simple harmonic motion is π/26 s
•  New equilibrium position is at 30 cm from P₁ and time period of simple harmonic motion is π/26 s

Solution

Q10. A block of mass m, attached to a fixed position O on a smooth inclined wedge of mass M, oscillates with amplitude A and linear frequency f. The wedge is located on a rough horizontal surface. If the angle of the wedge is 60°, then the force of friction acting on the wedge is given by (coefficient of static friction =μ)

•  μ(M+m)g
•  1/2 mω² A sin⁡ωt
•  μ[(M+m)g+√3/2 mω² A sin⁡ωt ]
•  μ(M+m) ω² Asin ωt

Solution