Question 2 :
What is the position of centre of gravity of a cylinder?<br/>

Question 4 :
The energy of electron in an excited hydrogen atom&#160;is -3.4 eV. Its angular momentum according to Bohr's theory will be:<br/>

Question 6 :
Where is the centre of gravity of a uniform ring situated ?<br/>

Question 7 :
A solid sphere is rolling down on inclined on plane from rest and a rectangular block of same mass is also slipping down simultaneously from rest on a similar smooth inclined plane.

Question 10 :
The centre of gravity of an object is ______ whether it is placed near the surface of the Earth or near the surface of the Moon.

Question 11 :
If&#160;$\displaystyle \vec{a}$ and $\vec{b}$ are two vectors then the value of&#160;$\displaystyle \left ( \vec{a}+\vec{b} \right )\times \left ( \vec{a}-\vec{b} \right )$ is:

Question 12 :
<p>A uniform heavy disc of moment of inertia $\displaystyle{I_1}$ is rotating with constant angular velocity $\displaystyle{\omega_1}$. Then, a second nonrotating disc of moment of inertia $\displaystyle{I_2}$ is dropped on it. The two discs rotate together. The final angular velocity of the system becomes</p>

Question 13 :
Let $\vec{F}$ be the force acting on a particle having position vector $\vec{r}$ and $\vec{\tau}$ be the torque of this force about the origin then:<br>

Question 15 :
Let $\overrightarrow{a}={a}_{1}\hat{i}+{a}_{2}\hat{j}+{a}_{3}\hat{k},\overrightarrow{b}={b}_{1}\hat{i}+{b}_{2}\hat{j}+{b}_{3}\hat{k},\overrightarrow{c}={c}_{1}\hat{i}+{c}_{2}\hat{j}+{c}_{3}\hat{k}$.If $\left|\overrightarrow{c}\right|=1$ and $\left(\overrightarrow{a}\times \overrightarrow{b}\right)\times \overrightarrow{c}=0$ then<br>${\left|\begin{matrix} {a}_{1} &amp; {a}_{2} &amp; {a}_{3} \\ {b}_{1} &amp;{b}_{2} &amp;{b}_{3} \\ {c}_{1} &amp;{c}_{2} &amp; {c}_{3} \end{matrix}\right|}^{2}=$<br>

Question 16 :
A symmetrical body of mass $M$, radius $R$ and&#160;radius of gyration $k$ is rolling on a horizontal&#160;surface without slipping. If linear velocity of centre&#160;of mass is $v_{c}$ and angular velocity is $\omega$; then:<br/>

Question 17 :
Match List I with List II from the combinations shown.<br>List - I<br>a)Addition of vectors <br>b)dot product <br>c) cross product <br>d) subtraction of Vectors <br><br>List - II<br>e)relative velocity<br>f)resultant velocity<br>g)work done <br>h) torque vectors <br><br>The correct match is

Question 18 :
A Proton of mass $1.6\times 10^{-27} $ kg goes round in a circular orbit of radius 0.1 metre under a centripetal force of $6\times 10^{-14} N$ then the frequency of revolution of proton is about ?

Question 19 :
A yo-yo is relased from your hand with the string wrapped around your finger. If you hold your hand still, the acceleration of the yo-yo is :&#160;

Question 20 :
A wheel of radius $R$ is free to rotate about its own&#160;axis. A tangential force $F$ is applied on the wheel&#160;along its rim. If $q$ is the angular displacement of&#160;wheel due to the force $F$, then work done by $F$ is:<br/>

Question 21 :
A rigid body is in pure rotation, that is, undergoing fixed axis rotation. Then which of the following statement(s) are true?

Question 22 :
A solid cylinder is placed on the end of an inclined plane. It is found that the plane can be tipped at an angle $\theta$ before the cylinder starts to slide. When the cylinder turns on its sides and is allowed to roll, it is found that the steepest angle at which the cylinder performs pure rolling is $\phi$. The ratio $tan\phi : tan\theta$ is:

Question 23 :
A wheel of radius $0.5 \ m$ rolls without sliding on a horizontal surface, starting from rest, the wheel moves with constant acceleration&#160;$\displaystyle 6\ { rad }/{ { s }^{ 2 } }$. The distance travelled by the centre of the wheel from $t=0$ to $t=3\ s$ is:

Question 24 :
A slender uniform rod of mass $M$ and length $l$ is provided at one end so that it can rotate in a vertical plane$.$ There is negligible friction at the pivot$.$ The free end is held vertically above the pivot and then released$.$ The angular acceleration of the rod when it makes an angle $\theta $ with me

Question 25 :
A cord is wound around the circumference of a bicycle wheel (without tyre) of diameter $1 &#160;m$. A mass of $2 &#160;kg$ is tied to the end of the cord and it is allowed to fall from rest. The weight falls $2 &#160;m$ in $4 &#160;s$. The axle of the wheel is horizontal and the wheel rotates with its plane vertical. The angular acceleration produced is:(take $g=10 &#160;ms^{-2}$)&#160;<br/>