Advertisements
Advertisements
Question
The velocity of bob of a second’s pendulum when it is 6 cm from its mean position and amplitude of 10 cm, is ______.
Options
8π cm/s
6π cm/s
4π cm/s
2π cm/s
Advertisements
Solution
The velocity of bob of a second’s pendulum when it is 6 cm from its mean position and amplitude of 10 cm, is 8π cm/s.
Explanation:
The velocity of the bob in simple harmonic motion is given by:
`v = omega sqrt(A^2 - x^2)`
Where:
A = 10 cm (amplitude),
x = 6 cm (displacement),
`omega = (2pi)/T`, with T = 2 s (second's pendulum), so ω = π rad/s.
Substitute the values:
`v = pisqrt(10^2 - 6^2)`
= `pi sqrt(100 - 36)`
= `pi sqrt64`
Simplify:
v = π × 8
= 8 π cm/s.
APPEARS IN
RELATED QUESTIONS
Obtain the expression for the period of a simple pendulum performing S.H.M.
A simple pendulum performs S.H.M. of period 4 seconds. How much time after crossing the mean position, will the displacement of the bob be one-third of its amplitude.
What is a second pendulum?
The length of a simple pendulum is increased by 44%. The percentage change in its time period is ______.
Work done in stretching a wire through 1 mm is 2 J. What amount of work will be done for elongating another wire of same material, with half the length and double the radius of cross-section, by 1 mm?
A simple pendulum has a time period T1 when on the earth's surface and T2 when taken to a height R above the earth's surface, where R is the radius of the earth. The value of T2 / T1 is ______.
A pendulum performs S.H.M. with period `sqrt3` second in a stationary lift. If lift moves up with acceleration `"g"/3`, the period of pendulum is ______. (g = acceleration due to gravity)
A simple pendulum has length 'L1'. When its amplitude is 'a' cm, its energy is 'E1'. When length is 2L1, its energy is 'E2' Amplitude is same for both the lengths The relation between E1 and E2 is ______.
A simple pendulum has a length of 2m and a bob of mass of 100 grams. It is whirled in a horizontal plane. If the string breaks under a tension of 10 N, the angle made by the string with vertical is ______
(g = 10 m/s2)
The maximum kinetic energy of a simple pendulum is 'K'. Its displacement in terms of amplitude 'a', when kinetic energy becomes `(K/2)` is ______.
The maximum frequency of transmitted radio waves above which the radio waves are no longer reflected back by ionosphere is ______.
(N = maximum electron density of lonosphere, g = acceleration due to gravity)
The bob of a simple pendulum performs SHM with period T in air and with period T1 in water Relation between T and T1 is ______.
(neglect friction due to water, density of the material of the bob is = `9/8xx10^3` kgm3, density of water = 1 gcc-1)
The ratio of frequencies of two oscillating pendulums is 3 : 2. Their lengths are in the ratio.
A pendulum bob is swinging in a vertical plane, such that its angular amplitude is less than 90°. At its highest point, the string is cut. Which trajectory is possible for bob afterwards?
The equation of motion in differential form for a seconds pendulum is ______.
A simple pendulum of length 196 cm performs linear SHM of amplitude 8 cm. Find the restoring force on its bob of mass 50 g at an extreme position.
A clock regulated by a second pendulum keeps the correct time. During winter the length of the pendulum decreases by 1 %. How much will the clock gain or lose in one day?
At the highest point of its swing, a simple pendulum has maximum potential energy and minimum kinetic energy. What is the total mechanical energy of the pendulum at any point during its motion?
A student measures time for 20 oscillations of a simple pendulum as 30 s, 32 s, 35 s and 35 s. If the minimum division in the measuring clock is 1 s, then correct mean time (in second) is ______.
A small sphere oscillates simple harmonically in a watch glass whose radius of curvature is 90 cm. The period of oscillations of the sphere is ______. (g = 10 ms−2)
If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is `x/2` times its original time period. Then the value of x is ______.
