A rod with rectangular cross section oscillates about a horizontal axis passing through one of its ends and it behaves like a seconds pendulum, its length will be
Text Solution
Verified by Experts
For disc `1 = MK^(2) = (MR^(2))/(2) rArr K = (R)/(sqrt(2)), l = R/2` `L = l + (K^(2))/(l) = (R)/(2) + (R^(2))/(2((R)/(2))) = R/2 + R = (3R)/(2) rArr T = 2pisqrt((L)/(g)) = 2pisqrt((3R)/(2g))`
Topper's Solved these Questions
SIMPLE HARMONIC MOTION
ALLEN |Exercise SOME WORKED OUT EXAMPLES|29 Videos
What will be the time period of seconds pendulum if its length is doubled?
The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I_(0) . Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is .............
A thin uniform metallic rod of length 0.5 m and radius 0.1 m rotates with an angular velocity 400rad/s is a horizontal plane about a vertical axis passing through one of its ends. Calculate (a) tenstion in the rod and (b) the elogation of te rod. The density of material of the rod is 10^(4)kg//m^(3) and the young's modulus is 2xx10^(11)N//m^(2)
A metallic rod of length I rotates at angular velocity omega about an axis passing through one end and perpendicular to the rod. If mass of electron is m and its charge is -e then the magnitude of potential difference between its two ends is
Figure shows the variation of the moment of inertia of a uniform rod, about an axis passing through itss centre and inclined at an angle theta to the length. The moment of inertia of the rod about an axis passing through one of its ends and making an angle theta=(pi)/(3) will be
Find the moment of inertia of ring about an axis passing through the centre and perpendicular to its plane.
A steel uniform rod of length 2L cross sectional area A and mass Mis set rotating in a horizontal plane about an axis passing through the centre. If Y is the Young's modulus for steel, find the extension in the length of the rod.
A uniform rod of mass m and length l rotates in a horizontal plane with an angular velocity omega about a vertical axis passing through one end. The tension in the rod at a distance x from the axis is
An almost inertia-less rod of length l3.5 m can rotate freely around a horizontal axis passing through its top end. At the bottom end of the roa a small ball of mass m andat the mid-point another small ball of mass 3m is attached. Find the angular frequency (in SI units) of small oscillations of the system about the equilibrium position. Gravitational acceleration is g=9.8 m//s^(2).
A wire of length L and cross section area A is kept on a horizontal surface and one of its end is fixed at point 0. A ball of mass m is tied to its other end and the system is rotated with angular velocity omega. Show that increase in its length. Delta l = (m omega ^(2) L ^(2))/(AY). Y is young’s modulus.