Advertisements
Advertisements
प्रश्न
A pendulum clock giving correct time at a place where g = 9.800 m/s2 is taken to another place where it loses 24 seconds during 24 hours. Find the value of g at this new place.
Advertisements
उत्तर
Let T1 be the time period of pendulum clock at a place where acceleration due to gravity \[\left( g_1 \right)\] is 9.8 ms−2.
Let T1 = 2 s
`g_1 = 9.8"ms"^(-2)`
Let T2 be the time period at the place where the pendulum clock loses 24 seconds during 24 hours.
Acceleration due to gravity at this place is \[\left( g_2 \right)\]
\[T_2 = \frac{24 \times 3600}{\frac{\left( 24 \times 3600 - 24 \right)}{2}}\]
\[ = 2 \times \frac{3600}{3599}\]
As
\[T \propto \frac{1}{\sqrt{g}}\]
\[\therefore \frac{T_1}{T_2} = \sqrt{\left( \frac{g_2}{g_1} \right)}\]
\[\Rightarrow \frac{g_2}{g_1} = \left( \frac{T_1}{T_2} \right)^2 \]
\[ \Rightarrow g_2 = \left( 9 . 8 \right) \left( \frac{3599}{3600} \right)^2 \]
\[ = 9 . 795 \text { m/ s}^2\]
APPEARS IN
संबंधित प्रश्न
The average displacement over a period of S.H.M. is ______.
(A = amplitude of S.H.M.)
A body of mass 1 kg is made to oscillate on a spring of force constant 16 N/m. Calculate:
a) Angular frequency
b) frequency of vibration.
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.
A pendulum clock gives correct time at the equator. Will it gain time or loose time as it is taken to the poles?
The average energy in one time period in simple harmonic motion is
A wall clock uses a vertical spring-mass system to measure the time. Each time the mass reaches an extreme position, the clock advances by a second. The clock gives correct time at the equator. If the clock is taken to the poles it will
Which of the following will change the time period as they are taken to moon?
(a) A simple pendulum
(b) A physical pendulum
(c) A torsional pendulum
(d) A spring-mass system
A small block oscillates back and forth on a smooth concave surface of radius R ib Figure . Find the time period of small oscillation.
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) t = 0.0125, (b) t = 0.025.
A particle is subjected to two simple harmonic motions, one along the X-axis and the other on a line making an angle of 45° with the X-axis. The two motions are given by x = x0 sin ωt and s = s0 sin ωt. Find the amplitude of the resultant motion.
Define the frequency of simple harmonic motion.
Write short notes on two springs connected in parallel.
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 the Earth as a homogeneous sphere of radius R and a straight hole is bored in it through its centre. Show that a particle dropped into the hole will execute a simple harmonic motion such that its time period is
T = `2π sqrt("R"/"g")`
A spring is stretched by 5 cm by a force of 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is ______
Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is ______.
- simple harmonic motion.
- non-periodic motion.
- periodic motion.
- periodic but not S.H.M.
A body having specific charge 8 µC/g is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V/m is applied horizontally toward the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be ______ s.
If x = `5 sin (pi t + pi/3) m` represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are ______.
