Download App

Rotational Mechanics — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsRotational Mechanics5 Marks
Question
A uniform rod pivoted at its upper end hangs vertically. It is displaced through an angle of $60^\circ$ and then released. Find the magnitude of the force acting on a particle of mass dm at the tip of the rod when the rod makes an angle of $37^\circ$ with the vertical.
✓

Answer


Let $l = $length of the rod, and $m =$ mass of the rod. Applying energy principle $\Big(\frac{1}{2}\Big)\text{l}\omega^2-0=\text{mg}\Big(\frac{1}{2}\Big)(\cos37^\circ-\cos60^\circ)$
$\Rightarrow\frac{1}{2}\times\frac{\text{ml}^2}{3}\omega^2$
$=\text{mg}\times\frac{1}{2}\Big(\frac{4}{5}-\frac{1}{2}\Big)\text{t}$
$\Rightarrow\omega^2=\frac{9\text{g}}{10\text{l}}=0.9\Big(\frac{\text{g}}{\text{l}}\Big)$
Again $\Big(\frac{\text{ml}^2}{3}\Big)\alpha=\text{mg}\Big(\frac{1}{2}\Big)\sin37^\circ=\text{mgl}\times\frac{3}{5}$
$\therefore\alpha=0.9\Big(\frac{\text{g}}{\text{l}}\Big)=$ angular acceleration.
So, to find out the force on the particle at the tip of the rod $F_i =$ centrifugal force $=(\text{dm})\omega^2\text{l}=0.9(\text{dm})\text{g} F_t =$ tangential force $=(\text{dm})\alpha\text{l}=0.9(\text{ dm})\text{g}$
So, total force $\text{F}=\sqrt{\big(\text{F}_{\text{i}}^2+\text{F}_{\text{t}}^2\big)}=0.9\sqrt2(\text{dm})\text{g}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Rotational Mechanics→Rotational Mechanics — all question types→Physics STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

A disc of radius R is cut out from a larger disc of radius 2R in such a way that the edge of the hole touches the edge of the disc. Locate the centre of mass of the residual disc.
→
How many time constants will elapse before the energy stored in the capacitor reaches half of its equilibrium value in a charging RC circuit?
→
Assuming an electron is confined to a 1nm wide region , find the uncertainty in momentum using Heisenberg Uncertainty principle (Ref Eq 11.12 of NCERT Textbook). You can assume the uncertainty in position $\Delta\text{x}$ as 1nm. Assuming $\text{p}\Box\Delta\text{p}$, find the energy of the electron in electron volts.
→
Two parallel wires seprated by a distance of 10cm carry currents of 10A and 40A along-the same direction. Where should a third current be placed so that it experiences no magnetic force?
→
An angular magnification $($magnifying power$)$ of $30X$ is desired using an objective of focal length $1.25 \ cm$ and an eyepiece of focal length $5 \ cm$. How will you set up the compound microscope?
→
A car goes on a horizontal circular road of radius R, the speed increasing at a constant rate $\frac{\text{d}\nu}{\text{dt}}=\text{a}.$ The friction dt coefficient between the road and the tyre is $\mu.$ Find the speed at which the car will skid.
→
A converging lens of focal length 15cm and a converging mirror of focal length 10cm are placed 50cm apart with common principal axis. A point source is placed in between the lens and the mirror at a distance of 40cm from the lens. Find the locations of the two images formed.
→
A metallic ring of mass m and radius l (ring being horizontal) is falling under gravity in a region having a magnetic field. If z is the vertical direction, the z-component of magnetic field is $\text{B}_\text{z}=\text{B}_0(1+\lambda\text{z})$. If R is the resistance of the ring and if the ring falls with a velocity v, find the energy lost in the resistance. If the ring has reached a constant velocity, use the conservation of energy to determine v in terms of $\text{m},\text{B},\lambda$ and acceleration due to gravity g.
→
  1. Define mutual inductance and write its $S.I$. unit.
  2. Derive an expression for the mutual inductance of two long co $-$ axial solenoids of same length wound one over the other.
  3. In an experiment, two coils $c_1 $ and $c_2$ are placed close to each other. Find out the expression for the emf induced in the coil $c_1$ due to a change in the current through the coil $c_2$.
→
$A 2\ kg$ block is placed over a $4\ kg$ block and both are placed on a smooth horizontal surface. The coefficient of friction between the blocks is $0.20.$ Find the acceleration of the two blocks if a horizontal force of $12N$ is applied to:
  1. The upper block.
  2. The lower block. Take $g = 10\ m/s^2.$
→