If the length of a pendulum is made $9$ times and mass of the bob is made $4$ times then the value of time period becomes
Easy
Download our app for free and get started
(a) $T = 2\pi \sqrt {\frac{l}{g}} $
==> $T \propto \sqrt l ,$
hence if l made $9$ times $T$ becomes $3$ times.
Also time period of simple pendulum does not depends on the mass of the bob.
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 performing simple harmonic motion along $x$ -axis with amplitude $4\, cm$ and time period $1.2\, sec$. The minimum time taken by the particle to move from $x = 2\, cm$ to $x =+ 4 \,cm$ and back again is given by .... $s$View Solution
- 2A block is resting on a piston which executes simple harmonic motion with a period $2.0 \,s$. The maximum velocity of the piston, at an amplitude just sufficient for the block to separate from the piston is .......... $ms ^{-1}$View Solution
- 3The angular frequency of the damped oscillator is given by, $\omega = \sqrt {\left( {\frac{k}{m} - \frac{{{r^2}}}{{4{m^2}}}} \right)} $ where $k$ is the spring constant, $m$ is the mass of the oscillator and $r$ is the damping constant. If the ratio $\frac{{{r^2}}}{{mk}}$ is $8\%$, the change in time period compared to the undamped oscillator is approximately as followsView Solution
- 4Two particles $P$ and $Q$ describe simple harmonic motions of same period, same amplitude, along the same line about the same equilibrium position $O.$ When $P$ and $Q$ are on opposite sides of $O$ at the same distance from $O$ they have the same speed of $1.2 \,m/s$ in the same direction, when their displacements are the same they have the same speed of $1.6\, m/s$ in opposite directions. The maximum velocity in $m/s$ of either particle isView Solution
- 5Two masses, both equal to $100\, g$, are suspended at the ends of identical light strings of length $\lambda = 1.0\, m$, attached to the same point on the ceiling (see figure). At time $t = 0$, they are simultaneously released from rest, one at angle $\theta_1 = 1^o$, the other at angle $\theta_2 = 2^o$ from the vertical. The masses will collideView Solution
- 6A particle moves on $x-$ axis according to the equation $x = x_0\,\,sin^2\,\omega t,$ the motion is simple harmonicView Solution
- 7Assume 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. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time periodView Solution
- 8If $A$ is the area of cross-section of a spring $L$ is its length $E$ is the Young's modulus of the material of the spring then time period and force constant of the spring will be respectivelyView Solution
- 9A particle is placed at the lowest point of a smooth wire frame in the shape of a parabola, lying in the vertical $xy-$ plane having equation $x^2 = 5y$ $(x, y$ are in meter). After slight displacement, the particle is set free. Find angular frequency of oscillation.....$rad/s$ (in $rad/sec$ ) (take $g = 10\ m/s^2$ )View Solution
- 10The springs shown are identical. When $A = 4kg$, the elongation of spring is $1\, cm$. If $B = 6\,kg$, the elongation produced by it is ..... $ cm$View Solution
