Advertisements
Advertisements
प्रश्न
Motion of an oscillating liquid column in a U-tube is ______.
विकल्प
periodic but not simple harmonic.
non-periodic.
simple harmonic and time period is independent of the density of the liquid.
simple harmonic and time-period is directly proportional to the density of the liquid.
Advertisements
उत्तर
Motion of an oscillating liquid column in a U-tube is simple harmonic and time period is independent of the density of the liquid.
Explanation:
If the liquid in U-tube is filled to a height of h and the cross-section of the tube is uniform and the liquid is incompressible and non-viscous. Initially, the level of liquid in the two limbs will be at the same height equal to h. If the liquid is pressed by y in one limb, it will rise by y along the length of the tube in the other limb, so the restoring force will be developed by the hydrostatic pressure difference
Here, the hydrostatic pressure provides the restoring force, thus,
F = – V.p.g
= – A.2ypg, where,
A = Area of a cross-section of tube and F ∝ – y,
Thus, it is a simple harmonic motion.
T = `sqrt((2πm("inertia"))/(k("spring"))`
= `sqrt((2πA(2h))/(p2Apg))`
T = `2π sqrt(h/g)`
Thus, the motion is harmonic as the time period is independent of density.
APPEARS IN
संबंधित प्रश्न
The maximum speed and acceleration of a particle executing simple harmonic motion are 10 cm/s and 50 cm/s2. Find the position(s) of the particle when the speed is 8 cm/s.
A block suspended from a vertical spring is in equilibrium. Show that the extension of the spring equals the length of an equivalent simple pendulum, i.e., a pendulum having frequency same as that of the block.
A block of mass 0.5 kg hanging from a vertical spring executes simple harmonic motion of amplitude 0.1 m and time period 0.314 s. Find the maximum force exerted by the spring on the block.
A body of mass 2 kg suspended through a vertical spring executes simple harmonic motion of period 4 s. If the oscillations are stopped and the body hangs in equilibrium find the potential energy stored in the spring.
The block of mass m1 shown in figure is fastened to the spring and the block of mass m2 is placed against it. (a) Find the compression of the spring in the equilibrium position. (b) The blocks are pushed a further distance (2/k) (m1 + m2)g sin θ against the spring and released. Find the position where the two blocks separate. (c) What is the common speed of blocks at the time of separation?
The spring shown in figure is unstretched when a man starts pulling on the cord. The mass of the block is M. If the man exerts a constant force F, find (a) the amplitude and the time period of the motion of the block, (b) the energy stored in the spring when the block passes through the equilibrium position and (c) the kinetic energy of the block at this position.
Repeat the previous exercise if the angle between each pair of springs is 120° initially.
Solve the previous problem if the pulley has a moment of inertia I about its axis and the string does not slip over it.
A 1 kg block is executing simple harmonic motion of amplitude 0.1 m on a smooth horizontal surface under the restoring force of a spring of spring constant 100 N/m. A block of mass 3 kg is gently placed on it at the instant it passes through the mean position. Assuming that the two blocks move together, find the frequency and the amplitude of the motion.
When the displacement of a particle executing simple harmonic motion is half its amplitude, the ratio of its kinetic energy to potential energy is ______.
If a body is executing simple harmonic motion and its current displacements is `sqrt3/2` times the amplitude from its mean position, then the ratio between potential energy and kinetic energy is:
A body is executing simple harmonic motion with frequency ‘n’, the frequency of its potential energy is ______.
A body is executing simple harmonic motion with frequency ‘n’, the frequency of its potential energy is ______.
A body is executing simple harmonic motion with frequency ‘n’, the frequency of its potential energy is ______.
Draw a graph to show the variation of P.E., K.E. and total energy of a simple harmonic oscillator with displacement.
A body of mass m is attached to one end of a massless spring which is suspended vertically from a fixed point. The mass is held in hand so that the spring is neither stretched nor compressed. Suddenly the support of the hand is removed. The lowest position attained by the mass during oscillation is 4 cm below the point, where it was held in hand.
What is the amplitude of oscillation?
A particle undergoing simple harmonic motion has time dependent displacement given by x(t) = A sin`(pit)/90`. The ratio of kinetic to the potential energy of this particle at t = 210s will be ______.
The total energy of a particle, executing simple harmonic motion is ______.
where x is the displacement from the mean position, hence total energy is independent of x.
