Let I be the moment of inetia of a uniform square plate about an … - Vidyadip

MCQ

Let $I$ be the moment of inetia of a uniform square plate about an axis $AB$ that passes though its centre and is parallel to two of its sides. $CD$ is a line in the plane of the plate that passes through the centre of the plate and makes an angle $\theta $ with $AB$ . The moment of inertia of the plate about the axis $CD$ is then equal to

✓
$I$
B
$I\,{\cos ^2}\theta $
C
$I\,{\sin ^2}\theta $
D
$I\,{\cos ^2}(\theta /2)$

✓

Answer

Correct option: A.

$I$

a
According to the perpendicular axes theorem

$I_{z}=I_{x}+I_{y}$

since the plate is quite symmetrical about

$AB$ and $CD$ we can use again perpendicular axes theorem

$I_{A B}=I_{C D}=I$

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 "M.C.Q (1 Marks)" from 6. system of particles and rotational motion→6. system of particles and rotational motion — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A clamped string is oscillating in $n^{th}$ harmonic, then

The amplitude of a particle executing $SHM$ is $4 \,cm$. At the mean position the speed of the particle is $16\, cm/sec$. The distance of the particle from the mean position at which the speed of the particle becomes $8\sqrt 3 \,cm/s,$ will be .... $cm$

In Melde's experiment, the string vibrates in $4$ loops when a $50 \,gram$ weight is placed in the pan of weight $15\, gram.$ To make the string to vibrates in $6$ loops the weight that has to be removed from the pan is

A uniform metal chain of mass $m$ and length ' $L$ ' passes over a massless and frictionless pulley. It is released from rest with a part of its length ' $l$ ' is hanging on one side and rest of its length ' $L -l$ ' is hanging on the other side of the pulley. At a certain point of time, when $l=\frac{L}{x}$, the acceleration of the chain is $\frac{g}{2}$. The value of $x$ is ........

If a gymnast sitting on a rotating stool with his arms outstretched, suddenly lowers his hands:

In stretching a spring by $2\,cm$ energy stored is given by $U,$ then more stretching by $10\,cm$ energy stored will be

The displacement of a particle varies with time according to the relation : $\text{y}=\text{a}\sin\omega\text{t}+\text{b}\cos\omega\text{t}$

A wire of cross-sectional area $3\,m{m^2}$ is first stretched between two fixed points at a temperature of $20°C$. Determine the tension when the temperature falls to $10°C$. Coefficient of linear expansion $\alpha = {10^{ - 5}} { ^\circ}{C^{ - 1}}$ and $Y = 2 \times {10^{11}}\,N/{m^2}$ ........ $N$

A block of $7\,kg$ is placed on a rough horizontal surface and is pulled through a variable force $F$ (in $N$ ) $= 5\,t$ , where $'t'$ is time in second, at an angle of $37^o$ with the horizontal as shown in figure. The coefficient of static friction of the block with the surface is one. If the force starts acting at $t = 0\,s$ . Find the time at which the block starts to slide ......... $\sec$ (Take $g = 10\,m/s^2$ )

A $2 \mathrm{~kg}$ brick begins to slide over a surface which is inclined at an angle of $45^{\circ}$ with respect to horizontal axis. The co-efficient of static friction between their surfaces is: