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The moment of inertia of a rod of lengh $l$ about an axis passing through its centre of mass and perpendicular to the rod is $I$. The moment of inertia of hexagonal shape formed by six such rods, about an axis passing through its centre of mass and perpendicular to its plane will be

What is kgf unit and how can we calculate it?

A non-zero force is acting on a body but work done is zero. Which of the following statements justify the above situation?

1.Displacement is zero.
2.Force is perpendicular to the direction of displacement.
3.Force is parallel to displacement.
4.Force is opposite to the direction of displacement.

Directions:- Study the following information carefully to answer the question given below.

Seven persons – A, B, C, D, E, F and G are standing in a straight line facing north at equal distances but not necessarily in the same order. Each of them is a different professional viz. Actor, Reporter, Doctor, Engineer, Teacher and Painter but not necessarily in the same order.
G is standing at the fifth position to the left of C. Reporter is standing at the third position to the right of G. F is standing at the fifth position to the right of A. E is standing second to the left of B. Engineer is standing at the second position to the left of D. Three persons are sitting between the Engineer and the Painter. The Doctor is to the immediate left of the Engineer. The Lawyer is to the immediate right of the Teacher.

Which of the following pairs of persons is sitting at the extreme ends?

For a given medium, the polarizing angle is ${60}^{\circ }$. The critical angle for this medium is

$\left({\sin }^{-1}\right(0.5773)={35}^{\circ }{16}^{\prime }\text{and}{\sin }^{-1}(0.886)={60}^{\circ })$

If a car covers $\frac{2}{5^{th}}$ of the total distance with $v_1$ speed and $\frac{3}{5^{th}}$ distance with $v_2$ then average speed is

If acceleration (a), velocity (v) and force (F) are used as fundamental quantities , represent Young’s modulus in term of these fundamental quantities.

A coil of inductance
0.50 H and resistance 100 Ω is
connected to a 240 V, 50 Hz ac supply.

(a) What is the
maximum current in the coil?

(b) What is the
time lag between the voltage maximum and the current maximum?

An insect crawl up a hemispherical surface very slowly (see Fig.). The coefficient of friction between the insect and the surface is $\frac{1}{3}$. If the line joining the center of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ is the given by

A charged body is kept in an electric field where it experiences a constant acceleration of 10 m/$s^2$ in the positive x-direction. The body hits wall after travelling 4 m and rebounds but can travel only upto 2 m before coming to rest momentarily . If the body was in contact with the wall for 12 ms then find the average acceleration of it due to the impact?

A particle is projected from the bottom of an inclined plane of angle ${30}^{\circ }$ with a velocity of $30\text{m/s}$ at an angle of ${60}^{\circ }$ with the horizontal. Find the distance travelled by the particle along the plane before it hits the plane.

On seeing a board of speed limit, you apply brakes that brings the car from speed of $90\text{km/h}$ to a speed of $72\text{km/h}$, covering a distance of $150\text{m}$ at a constant acceleration. How much time is required for the given decrease in speed?

A particle of mass $1\text{kg}$ is fastened to one end of a string of length $2\text{m}$ and a mass $2\text{kg}$ is attached to the middle point, the other end of the string is fastened to a fixed point on a smooth horizontal table. The particles are then projected so that the two portions of the string are always in the same straight line and describes horizontal circles. Then the ratio of tensions $\left(\frac{T_1}{T_2}\right)$ in the two parts of the string as shown in diagram is

The angular velocity of a particle moving in a circle of radius $50cm$ is increased in $5$ min from $100$ revolutions per minute to $400$ revolutions per minute. Find the tangential acceleration of the particle.

Let $\overrightarrow{a}=\hat{i}+2\hat{j}-3\hat{k}$ and $\overrightarrow{b}=2\hat{i}-3\hat{j}+5\hat{k}.$ If $\overrightarrow{r}\times \overrightarrow{a}=\overrightarrow{b}\times \overrightarrow{r},$ $\overrightarrow{r}\cdot (\alpha \hat{i}+2\hat{j}+\hat{k})=3$ and $\overrightarrow{r}\cdot (2\hat{i}+5\hat{j}-\alpha \hat{k})=-1,$ $\alpha \in R,$ then the value of $\alpha +|\overrightarrow{r}{|}^2$ is equal to :

A charged particle enters a uniform magnetic
field with velocity vector at an angle of 45⁰ with the magnetic
field. The pitch of the helical path followed by the particle is p. The radius
of the helix will be

The combination of gates shown below yields

Two uniform rods AB and BC have Young's modulii $1.2\times {10}^{11}N/m^2\text{and}1.5\times {10}^{11}N/m^2$ respectivey. If coefficient of linear expansion of AB is $1.5\times {10}^{-5}/°C$ and both have equal area of cross section, then coefficient of linear expansion of BC, for which there is not shift of the junction at all temperatures, is

During the phase change of a pure substance

The maximum acceleration of a body moving in SHM is $a_0$ and maximum velocity is $v_0$. The amplitude of the oscillation is given by,

A vector has component along the $x$-axis equal to $25\text{unit}$ and along the $y$-axis equal to $60\text{unit}$. Then the position vector will be

A wheel (to be considered as a ring) of mass $m$ and radius $R$, rolls without sliding on a horizontal surface, with constant velocity $V_0$. It encounters a stop of height $R/2$ at which it ascends without sliding. The angular velocity of the ring just after it comes in contact with the step is,

A block of mass $m_1=0.5\text{kg}$ is moving with the speed of $u_1=2\text{m/s}$ on a smooth surface. It strikes another mass of $m_2=1\text{kg}$ initially at rest and then they move together as a single body. The energy lost during the collision is

Thermal conductivity is lower for

Charges $Q_1$ and $Q_2$ are at points $A$ and $B$ of a right angle triangle $OAB$ see figure. The resultant electric feild at point $O$ is perpendicular to the hypotenuse, then $Q_1/Q_2$ is proportional to :

For a gas sample with $N_0$ number of molecules, function $N\left(V\right)$ is given by $N\left(V\right)=\frac{dN}{dV}=\left(\frac{3N_0}{V_0^3}\right)V^2$ for $0<V<V_o$ and $N\left(V\right)=0$ for $V>V_0$ where dN is the number of molecules in the speed range $V$ to $V+dV$. The rms speed of the molecules is

If a magnet is suspended at an angle ${30}^{\circ }$ to the magnetic meridian, it makes an angle of ${45}^{\circ }$ with the horizontal. The real dip is

A bullet of mass 20g travelling horizontally with a speed of 500 m/s passes through a wooden block of mass 10.0 kg initially at rest on a level surface. The bullet emerges with a speed of 100 m/s and the block slides 20 cm on the surface before coming to rest. The friction coefficient between the block and the surface is $g=10m{s}^{-2}$

Four charges of $6\mu \text{C},2\mu \text{C},-12\mu \text{C}\text{and}4\mu \text{C}$ are placed at the corners of a square of side $1\text{m}$. The square is in xy-plane and its center at its origin. Electric potential due to these charges is zero everywhere on the line

A simple pendulum of bob mass m is oscillating with an angular amplitude ${\alpha }_m$ (in radian). The maximum tension in the string is

A ray of light is incident on a medium with angle of incidence $i$ and refracted into a second medium with angle of refraction $r$. The graph of $\sin \left(i\right)\text{vs}\sin \left(r\right)$ is shown in figure.

If the first medium is air, then the velocity of light in the second medium will be (Take $c=3\times {10}^8{\text{ms}}^{-1}$)