Mass is distributed uniformly over a thin rectangular plate and p… - Vidyadip

MCQ

Mass is distributed uniformly over a thin rectangular plate and positions of two vertices are given by $(1, 3)$ and $(2, -4)$. What is the position of $3^{rd}$ vertex if centre of mass of the plate lies at the origin ?

A
$(1, -2)$
B
$(-2, 4)$
✓
$(-3, 1)$
D
$(1, 2)$

✓

Answer

Correct option: C.

$(-3, 1)$

c
$\left(\mathrm{x}_{\mathrm{CM}}, \mathrm{y}_{\mathrm{CM}}\right)=\left(\frac{\mathrm{x}_{1}+\mathrm{x}_{2}+\mathrm{x}_{3}}{3}, \frac{\mathrm{y}_{1}+\mathrm{y}_{2}+\mathrm{y}_{3}}{3}\right)$

$(0,0)=\left(\frac{1+2+x_{3}}{3}, \frac{3-4+y_{3}}{3}\right)$

$\left(\mathrm{x}_{3}, \mathrm{y}_{3}\right)=(-3,1)$

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

$PV$ versus $T$ graph of equal masses of ${H_2}$, $He$ and ${O_2}$ is shown in fig. Choose the correct alternative

Two protons $A$ and $B$ move parallel to the $x$-axis in opposite directions with equal speeds $v$. At the instant shown, the ratio of magnetic force and electric force acting on the proton $A$ is ( $c=$ speed of light in vacuum)

In hydrogen atom, an electron is revolving in the orbit of radius $0.53\,{\mathop A\limits^o }$ with $6.6 \times {10^{15}}$ $rotations/second$. Magnetic field produced at the centre of the orbit is.......$wb/{m^2}$

Plane figures made of thin wires of resistance $R = 50$ milli ohm/metre are located in a uniform magnetic field perpendicular into the plane of the figures and which decrease at the rate $dB/dt =\, 0.1 \,m \,T/s$. Then currents in the inner and outer boundary are. (The inner radius $a = 10 \,cm$ and outer radius $b = 20 \,cm$)

A force vector applied on a mass is represented as $\vec F = 6\hat i - 8\hat j + 10\hat k$ and accelerates with $1\;m/{s^2}$. What will be the mass of the body in $kg$.

A uniform solid sphere of mass $m$ is being pulled on a horizontal surface with force $F$ parallel to the surface and applied at its top most point. If the acceleration of the cylinder is $a$ & it is rolling on the surface, the value of $F$ is

Let $\bar v,\;{v_{rms}}$ and ${v_p}$ respectively denote the mean speed, root mean square speed and most probable speed of the molecules in an ideal monoatomic gas at absolute temperature $T.$ The mass of a molecule is $m.$ Then

A ball is dropped from height $5\,\,m$. The time after which ball stops rebounding if coefficient of restitution between ball and ground $e = 1/2$, is ............. $\mathrm{sec}$

If $N$ is the number of turns in a coil, the value of self-inductance varies as

Consider two identical cylinders [each of mass $m$ density $\rho _0$ horizontal cross-section area $s$] in equilibrium, partially submerged in two containers filled with liquids of densities $\rho_1$ and $\rho_2$ as shown in figure. Find the period of small oscillations of this system about its equilibrium. Neglect the changes in the level of liquids in the containers. Neglect mass of the strings. acceleration due to gravity is $g$ . ($v$ is volume of each block)