Question:
A rigid massless rod of length $3 l$ has two masses attached at each end as shown in the figure. The rod is pivoted at point $\mathrm{P}$ on the horizontal axis (see figure). When released from initial horizontal position, its instantaneous angular acceleration will be:
$\frac{\mathrm{g}}{13 l}$
$\frac{\mathrm{g}}{3 l}$
$\frac{\mathrm{g}}{2 l}$
$\frac{7 \mathrm{~g}}{3 l}$
Question of from chapter.
JEE Main Previous Year 10 Jan. 2019
Correct Option: 1
Solution:
Related Questions
A rod of length $L$ has non-uniform linear mass density given by $\rho(x)=a+b\left(\frac{x}{\mathrm{~L}}\right)^{2}$, where $a$ and $b$ are constants and $0 \leq x \leq \mathrm{L}$. The value of $x$ for the centre of mass of the rod is at:
The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plale) of mass $4 \mathrm{~kg}$. (The coordinates of the same are shown in figure) are:
As shown in fig. when a spherical cavity (centred at $O$ ) of radius 1 is cut out of a uniform sphere of radius $R$ (centred at $C$ ), the centre of mass of remaining (shaded) part of sphere is at $G$, i.e on the surface of the cavity. $R$ can be determined by the equation:
Three point particles of masses $1.0 \mathrm{~kg}, 1.5 \mathrm{~kg}$ and $2.5 \mathrm{~kg}$ are placed at three corners of a right angle triangle of sides $4.0 \mathrm{~cm}, 3.0 \mathrm{~cm}$ and $5.0 \mathrm{~cm}$ as shown in the figure. The center of mass of the system is at a point:
Three particles of masses $50 \mathrm{~g}, 100 \mathrm{~g}$ and $150 \mathrm{~g}$ are placed at the vertices of an equilateral triangle of side $1 \mathrm{~m}$ (as shown in the figure). The $(x, y)$ coordinates of the centre of mass will be :
Four particles A, B, C and D with masses $m_{\mathrm{A}}=m, m_{\mathrm{B}}=$ $2 \mathrm{~m}, m_{\mathrm{C}}=3 \mathrm{~m}$ and $m_{\mathrm{D}}=4 \mathrm{~m}$ are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is :
A uniform rectangular thin sheet $\mathrm{ABCD}$ of mass $\mathrm{M}$ has length a and breadth $b$, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be :
The position vector of the centre of mass $r_{\mathrm{cm}}$ of an asymmetric uniform bar of negligible area of crosssection as shown in figure is:
A force of $40 \mathrm{~N}$ acts on a point $\mathrm{B}$ at the end of an $\mathrm{L}$-shaped object, as shown in the figure. The angle $\theta$ that will produce maximum moment of the force about point $A$ is given by:
In a physical balance working on the principle of moments, when $5 \mathrm{mg}$ weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?