A simple pendulum of length 1 m and having a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The bob of the simple pendulum experiences both the acceleration due to gravity $(g)$ and the centripetal acceleration $(a_c = v^2/R)$ due to the

Vedclass · Accepted Answer

$101$

Vedclass · Answer

(C) The bob of the simple pendulum experiences both the acceleration due to gravity $(g)$ and the centripetal acceleration $(a_c = v^2/R)$ due to the circular motion of the car. These two accelerations are perpendicular to each other. The effective acceleration $(g')$ acting on the bob is given by $g' = \sqrt{g^2 + a_c^2} = \sqrt{g^2 + (v^2/R)^2} = \sqrt{g^2 + v^4/R^2}$. The time period of a simple pendulum is $T = 2\pi \sqrt{L/g'}$. Substituting the values: $T = 2\pi \sqrt{L / \sqrt{g^2 + v^4/R^2}} = 2\pi \sqrt{1 / (g^2 + v^4/R^2)^{1/2}} = 2\pi / (g^2 + v^4/R^2)^{1/4}$. Comparing this with $T = 2\pi / \alpha^{1/4}$,we get $\alpha = g^2 + v^4/R^2$. Given $g = 10 \ m/s^2$,$v = 10 \ m/s$,and $R = 100 \ m$: $\alpha = (10)^2 + (10)^4 / (100)^2 = 100 + 10000 / 10000 = 100 + 1 = 101$.

Similar Questions

The time period of a simple pendulum measured inside a stationary lift is found to be $T$. If the lift starts accelerating upwards with an acceleration $g/3$,the new time period is:

If the mass of a bob of a pendulum is increased by $9$ times, the period of the pendulum will?

$A$ pendulum has a time period $T$. If it is taken to another planet having an acceleration due to gravity half that of the Earth and a mass $9$ times that of the Earth,then its time period on the other planet will be:

$A$ simple pendulum oscillates freely between points $A$ and $B$. We now put a peg (nail) at the point $C$ as shown in the figure. As the pendulum moves from $A$ to the right,the string will bend at $C$ and the pendulum will go to its extreme point $D$. Ignoring friction,the point $D$

$A$ bob of a simple pendulum has mass $m$ and is oscillating with an amplitude $a$. If the length of the pendulum is $L$,then the maximum tension in the string is (given $\cos 0^{\circ}=1, g=$ acceleration due to gravity):

Vedclass Test Series

Exam Paper Generator

Online Exam Module