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
AI Generated Solution
To find the length of a rod with a rectangular cross-section that behaves like a seconds pendulum when oscillating about a horizontal axis passing through one of its ends, we can follow these steps:
### Step 1: Understand the Time Period Formula
The time period \( T \) for a rigid body oscillating about a pivot is given by the formula:
\[
T = 2\pi \sqrt{\frac{I}{mgd}}
\]
where:
...
A uniform rod of mass m. length L, area of cross- secticn A is rotated about an axis passing through one of its ends and perpendicular to its length with constant angular velocity \(omega\) in a horizontal plane If Y is the Young's modulus of the material of rod, the increase in its length due to rotation of rod is
The radius of gyration of an uniform rod of length l about an axis passing through one of its ends and perpendicular to its length is.
A thin uniform rod of mass M and length L is free to rotate in vertical plane about a horizontal axis passing through one of its ends. The rod is released from horizontal position shown in the figure. Calculate the shear stress developed at the centre of the rod immediately after it is released. Cross sectional area of the rod is A. [For calculation of moment of inertia you can treat it to very thin]
A thin uniform copper rod length l and mass m rotates unifomly with an angular velocity omega about a vertical axis passing through one of its ends as shown in the figure. Young's modulus of copper is Y. Breaking stress is sigma_(max) , cross sectional area of rod is A and density of rod is uniform. Based on above information, answer the following questions The maximum angular velocity with which the rod can rotate so that is won't break, is
A uniform rod of length 4l and mass m is free to rotate about a horizontal axis passing through a point distant l from its one end. When the rod is horizontal its angular velocity is omega as shown in figure. calculate (a). reaction of axis at this instant, (b). Acceleration of centre of mass of the rod at this instant. (c). reaction of axis and acceleration of centre mass of the rod when rod becomes vertical for the first time. (d). minimum value of omega , so that centre of rod can complete circular motion.
For an L shaped conducting rod placed in an uniform magnetic field vecB rotating with constant angular velocity omega about an axis passing through one of its ends A and normal to the plane of the conductor induced emf
A uniform rod of length l oscillates about an axis passing through its end. Find the oscillation period and the reduced length of this pendulum.
find the radius of gyration of a rod of mass m and length 2l about an axis passing through one of its ends and perpendicular to its length.
A thin uniform copper rod of length l and mass m rotates uniformly with an angular velocity omega in a horizontal plane about a vertical axis passing through one of its ends. Determine the tension in the rod as a function of the distance r from the rotation axis. Find the elongation of the rod.
The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its mid-point and perpendicular to its length is I_0 . Its moment of inertia about an axis passing through one of its ends perpendicular to its length is.