मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

A Particle Executes S.H.M. with a Period of 10 Seconds. Find the Time in Which Its Potential Energy Will Be Half of Its Total Energy. - Physics

Advertisements
Advertisements

प्रश्न

A particle executes S.H.M. with a period of 10 seconds. Find the time in which its potential energy will be half of its total energy.

Advertisements

उत्तर

Given: T = 10 s

P. E = `1/2 (T.E)`

To find: Time (t)

∴ t = 1.25 s

The time in which the potential energy will be half of total energy is 1.25 s.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2015-2016 (July)

APPEARS IN

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

A particle in S.H.M. has a period of 2 seconds and amplitude of 10 cm. Calculate the acceleration when it is at 4 cm from its positive extreme position.


Which of the following relationships between the acceleration a and the displacement x of a particle involve simple harmonic motion?

(a) a = 0.7x

(b) a = –200x2

(c) a = –10x

(d) a = 100x3


Can the potential energy in a simple harmonic motion be negative? Will it be so if we choose zero potential energy at some point other than the mean position?


The energy of system in simple harmonic motion is given by \[E = \frac{1}{2}m \omega^2 A^2 .\] Which of the following two statements is more appropriate?
(A) The energy is increased because the amplitude is increased.
(B) The amplitude is increased because the energy is increased.


Can a pendulum clock be used in an earth-satellite?


A student says that he had applied a force \[F = - k\sqrt{x}\] on a particle and the particle moved in simple harmonic motion. He refuses to tell whether k is a constant or not. Assume that he was worked only with positive x and no other force acted on the particle.


A particle moves on the X-axis according to the equation x = A + B sin ωt. The motion is simple harmonic with amplitude


Figure represents two simple harmonic motions.

The parameter which has different values in the two motions is


A pendulum clock that keeps correct time on the earth is taken to the moon. It will run


Which of the following quantities are always negative in a simple harmonic motion?

(a) \[\vec{F} . \vec{a} .\]

(b) \[\vec{v} . \vec{r} .\]

(c) \[\vec{a} . \vec{r} .\]

(d)\[\vec{F} . \vec{r} .\]


A particle moves on the X-axis according to the equation x = x0 sin2 ωt. The motion is simple harmonic


The angle made by the string of a simple pendulum with the vertical depends on time as \[\theta = \frac{\pi}{90}  \sin  \left[ \left( \pi  s^{- 1} \right)t \right]\] .Find the length of the pendulum if g = π2 m2.


Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance R/2 from the earth's centre where R is the radius of the earth. The wall of the tunnel is frictionless. (a) Find the gravitational force exerted by the earth on a particle of mass mplaced in the tunnel at a distance x from the centre of the tunnel. (b) Find the component of this force along the tunnel and perpendicular to the tunnel. (c) Find the normal force exerted by the wall on the particle. (d) Find the resultant force on the particle. (e) Show that the motion of the particle in the tunnel is simple harmonic and find the time period.


A simple pendulum of length 1 feet suspended from the ceiling of an elevator takes π/3 seconds to complete one oscillation. Find the acceleration of the elevator.


A simple pendulum fixed in a car has a time period of 4 seconds when the car is moving uniformly on a horizontal road. When the accelerator is pressed, the time period changes to 3.99 seconds. Making an approximate analysis, find the acceleration of the car.


A closed circular wire hung on a nail in a wall undergoes small oscillations of amplitude 20 and time period 2 s. Find (a) the radius of the circular wire, (b) the speed of the particle farthest away from the point of suspension as it goes through its mean position, (c) the acceleration of this particle as it goes through its mean position and (d) the acceleration of this particle when it is at an extreme position. Take g = π2 m/s2.


A particle is subjected to two simple harmonic motions given by x1 = 2.0 sin (100π t) and x2 = 2.0 sin (120 π t + π/3), where x is in centimeter and t in second. Find the displacement of the particle at (a) = 0.0125, (b) t = 0.025.


A particle executing SHM crosses points A and B with the same velocity. Having taken 3 s in passing from A to B, it returns to B after another 3 s. The time period is ____________.


Define the time period of simple harmonic motion.


Define the frequency of simple harmonic motion.


What is meant by simple harmonic oscillation? Give examples and explain why every simple harmonic motion is a periodic motion whereas the converse need not be true.


Consider a simple pendulum of length l = 0.9 m which is properly placed on a trolley rolling down on a inclined plane which is at θ = 45° with the horizontal. Assuming that the inclined plane is frictionless, calculate the time period of oscillation of the simple pendulum.


A body oscillates with SHM according to the equation x = 5 cos `(2π"t" + π/4)`. Its instantaneous displacement at t = 1 sec is:


The displacement of a particle varies with time according to the relation y = a sin ωt + b cos ωt.


Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is ______.

  1. simple harmonic motion.
  2. non-periodic motion.
  3. periodic motion.
  4. periodic but not S.H.M.

A weightless rigid rod with a small iron bob at the end is hinged at point A to the wall so that it can rotate in all directions. The rod is kept in the horizontal position by a vertical inextensible string of length 20 cm, fixed at its midpoint. The bob is displaced slightly, perpendicular to the plane of the rod and string. The period of small oscillations of the system in the form `(pix)/10` is ______ sec. and the value of x is ______.

(g = 10 m/s2)

 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×