In an experiment to determine the period of a simple pendulum of length $1\, m$, it is attached to different spherical bobs of radii $r_1$ and $r_2$ . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be $5\times10^{-4}\, s$, the difference in radii, $\left| {{r_1} - {r_2}} \right|$ is best given by .... $cm$
JEE MAIN 2017, Diffcult
Download our app for free and get started
As we know, Time-period of simple
pendulum, T $\propto \sqrt{l}$
$5 \times {10^{ - 4}} = \frac{1}{2}\frac{{{r_1} - {r_2}}}{1}$
$\because$ change in length $\Delta l=r_{1}-r_{2}$
$5 \times {10^{ - 4}} = \frac{1}{2}\frac{{{r_1} - {r_2}}}{1}$
$r_{1}-r_{2}=10 \times 10^{-4}$
$10^{-3} \mathrm{m}=10^{-1} \mathrm{cm}=0.1 \mathrm{cm}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A particle is doing simple harmonic motion of amplitude $0.06 \mathrm{~m}$ and time period $3.14 \mathrm{~s}$. The maximum velocity of the particle is. . . . .. . $\mathrm{cm} / \mathrm{s}$.View Solution
- 2A body is moving in a room with a velocity of $20\, m / s$ perpendicular to the two walls separated by $5$ meters. There is no friction and the collisions with the walls are elastic. The motion of the body isView Solution
- 3A body executes simple harmonic motion. The potential energy $(P.E.)$, the kinetic energy $(K.E.)$ and total energy $(T.E.)$ are measured as a function of displacement $x$. Which of the following statements is trueView Solution
- 4In the given figure, a body of mass $M$ is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant $k,$ the frequency of oscillation of given body is :View Solution
- 5The displacement y of a particle executing periodic motion is given by $y = 4{\cos ^2}(t/2)\sin (1000t)$. This expression may be considered to be a result of the superposition of ........... independent harmonic motionsView Solution
- 6In damped oscillations, damping force is directly proportional to speed of oscillator. If amplitude becomes half of its maximum value in $1 \,s$, then after $2 \,s$ amplitude will be $\left(A_0-\right.$ initial amplitude)View Solution
- 7The time period of a mass suspended from a spring is $T$. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will beView Solution
- 8Two bodies of masses $1\, kg$ and $4\, kg$ are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency $25\, rad/s$, and amplitude $1.6\, cm$ while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is ..... $N$ ( take $g = 10\, ms^{-2}$)View Solution
- 9In a linear simple harmonic motion $(SHM)$View Solution
$(A)$ Restoring force is directly proportional to the displacement.
$(B)$ The acceleration and displacement are opposite in direction.
$(C)$ The velocity is maximum at mean position.
$(D)$ The acceleration is minimum at extreme points.
Choose the correct answer from the options given below :
- 10A particle is executing $SHM$ along a straight line. Its velocities at distance $x_1$ and $x_2$ from the mean position are $V_1$ and $V_2$ respectively. Its time period isView Solution