MCQ
In a rectangle $ABCD\,\,(BC = 2AB)$. The moment of inertia along which axis will be minimum
- A$BC$
- B$BD$
- C$HF$
- ✓$EG$
✓
Answer
Correct option: D.
$EG$
d
The moment of inertia will be minimum about that axis, which is passing through the center of mass.
The moment of inertia will be minimum about that axis, which is passing through the center of mass.
$I_{E G}=\frac{M B^{2}}{12}$
$I_{F H}=\frac{M(2 B)^{2}}{12}=\frac{M B^{2}}{6}$
$M. I.$ of the rectangular plate about its diagonal $I_{B D}=\frac{M B^{2} L^{2}}{6\left(B^{2}+L^{2}\right)}=\frac{M B^{2} \times 4 B^{2}}{6\left(B^{2}+4 B^{2}\right)}=\frac{2}{15} M B^{2}=\frac{M B^{2}}{7.5}$
$M. I.$ about $E G$ is minimum.
$\mathrm{OR}$
By observation, distribution of mass is the nearest about axis $E G .$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The area of each plate of a parallel plate capacitor is $20\,cm^2$ and separation between the plates is $2\,mm$. If dielectric strength of air is $3 \times 10^6\,V/m,$ the maximum possible value of emf of the battery, which can be connected across the plates of this capacitor and the corresponding charge on the plates is
→A vessel contains $14 \,gm \,(7 $ moles) of hydrogen and $96\, gm$ ($9$ moles) of oxygen at $STP.$ Chemical reaction is induced by passing electric spark in the vessel till one of the gases is consumed. The temperature is brought back to it's starting value $273 K.$ The pressure in the vessel is ...... $atm$
→Two circuits $(a)$ and $(b)$ have charged capacitors of capacitance $C, 2C$ and $3C$ with open switches. Charges on each of the capacitor are as shown in the figures. On closing the switches
→A thermodynamic system is taken from an original state $A$ to an intermediate state $B$ by a linear process as shown in the figure. It's volume is then reduced to the original value from $B$ to $C$ by an isobaric process. The total work done by the gas from $A$ to $B$ and $B$ to $C$ would be :
→As the switch $S$ is closed in the circuit shown in figure, current passed through it is .................. $A$
→The figure shows variation of $R, X_L$ and $X_C$ with frequency f in a series $L, \,C, \,R $ circuit. Then for what frequency point, the circuit is inductive
→Figure shows two containers $P$ and $Q$ with same base area $A$ and each filled upto same height with same liquid. Select the correct alternative .............
→Magnetic fleld changing at the rate of $4\,T/sec$ in a circular region of $5\, cm$ radius. The value of induced electric field at a point $'P'$, which is $10\, cm$ distance away from the centre $'O'$ of region is .....$V/m$
→A thin square steel plate with each side equal to $10$ cm is heated by a blacksmith. The rate of radiated energy by the heated plate is $1134 W$ . The temperature of the hot steel plate is ....... $K$ (Stefan's constant $\sigma = 5.67 \times {10^{ - 8}}watt\;{m^{ - 2}}{K^{ - 4}}$, emissivity of the plate = $1$ )
→In $X-$ ray spectrum wavelength $\lambda$ of line ${K_\alpha }$ depends on atomic number $Z$ as
→