Question 3 :
<p>The dimension of $ \cfrac {1}{2}\epsilon_o E^2$ permittivity of free space and E:<br>Intensity of electric field) is </p><br><br><p> </p>

Question 4 :
Assertion: The number of significant figures depends on the least count of measuring instrument. Reason: Significant figures define the accuracy of measuring instrument.

Question 5 :
The speed of light ($c$), gravitational constant ($G$) and Planck's constant ($h$) are taken as&#160;fundamental units in a system. The dimensions of time in this new system should be

Question 6 :
A ball is thrown vertically upwards from the top of a tower with an initial velocity of $19.6 m {s}^{-1}$. The ball reaches the ground after $5 s$. Calculate :$(i)$ the height of the tower, $(ii)$ the velocity of ball on reaching the ground. Take $g=9.8 m {s}^{-2}$.

Question 7 :
A bullet penetrates a distance d of a plank. If the initial momentum of the bullet is doubled, the distance penetrated will be

Question 8 :
Two bodies are thrown vertically upward, with the same initial velocity of $98\ m/s$ but $4\ sec$ apart. How long after the first one is thrown when they meet ?

Question 9 :
Bullets of 0.03 kg mass each hit a plate at the&#160;rate of 200 bullets per second with a velocity of&#160;30 m/s. Their average force acting on the plate&#160;in newton is

Question 10 :
An object is placed on the surface of a smooth inclined plane of inclination $\theta$. It takes time $t$ to reach the bottom. If the same object is allowed to slide down a rough inclined plane of same inclination $\theta $, it takes times nth to reach the bottom where $n$ number greater than $1$. The coefficient of friction $\mu$ is given by:

Question 11 :
The relation $3t=\sqrt{3x}+6$ describes the displacement of a particle in one direction where $x$ is in meters and $t$ in seconds. The displacement when velocity is zero is:

Question 12 :
A car moving along a circular path of radius $R$ with uniform speed covers an angle $\theta$&#160;during&#160;a given&#160;time $t$.&#160;What is&#160;its&#160;average velocity?

Question 13 :
How much work is done in ergs in pulling a box 2 m across a tabletop with a force of 20 N in the horizontal direction?

Question 14 :
A stationary body explodes into four identical fragments such that three of them fly off mutually perpendicular to each other, each with same kinetic energy, $E_0$. The minimum energy of explosion will be

Question 15 :
One end of a uniform rod having mass m and length $l$ is hinged. The rod is placed on a smooth horizontal surface and rotates on it about the hinged end at a uniform angular velocity $\omega$. The force exerted by the hinge on the rod has a horizontal component equal to :

Question 16 :
AU the particles of a system are situated at a distance r from the origin. The distance of the centre of mass of the system from the origin is :

Question 17 :
A vertical steel post of diameter $25 cm$ and length $2.5 m$ supports a weight of $8000 kg$. Find the change in length produced.(Given $Y=2\times 10^{11}Pa$)<br/>

Question 18 :
The height at which the value of acceleration due to gravity becomes $50\% $ of that at the surface of the earth$.$ (radius of the earth =$6400 km$) is

Question 19 :
An artificial satellite of mass $m $&#160;is moving in circular orbit at a height equal to the radius $R$ of the earth. Suddenly due to internal explosion the satellite breaks into two parts of equal pieces. One part of the&#160;satellite stops just after the explosion. The increase in the mechanical energy of the system due to&#160;explosion will be (Given: acceleration due to gravity on the surface of earth is $g$)

Question 20 :
The escape velocity for a body projected vertically upwards from the surface of the earth is ${ 11.2 }{ km } { s }^{ -1 }$. If the body is projected in a direction making am angle ${ 45 }^0$ with the vertical, the escape velocity will be

Question 21 :
The velocity head of a stream of water is 40 cm.&#160;Then, the velocity of flow of water is :

Question 22 :
The amount of work done in an adiabatic expansion from temperature T to $T_{1}$ is

Question 23 :
$300$ gm of water at $25^o$C is added to $100$gm of ice at $0^oC$ . Final temperature of the mixture is:

Question 24 :
A wire of length $L _ { 0 }$ is supplied heat to raise its temperature by $T.$ if $\gamma$ is the coefficient of volume expansion of the wire and $Y$ is Young's modulus of the wire then the energy density stored in the wire is

Question 26 :
State whether true or false:Mean free path order for some gases at 273 K and 1 atm P is<br/>$He &gt; H_2 &gt; O_2 &gt; N_2 &gt; CO_2$

Question 27 :
RMS velocity of an ideal gas at $27^o C$ is $500{m/s}$, Temperature is increased four times, RMS velocity will become.

Question 28 :
A spring of force constant $k$ is cut into two equal parts, which are then joined parallel to each other. The force constant of the combination will be<br>

Question 29 :
If a simple pendulum of length $L$ has maximum angular displacement $\alpha$ then the maximum kinetic energy of bob of mass $M$ is

Question 30 :
A longitudinal wave is represented by $x=x_0\,sin\,2\pi(nt-\dfrac{\pi}{\lambda})$. The maximum particle velocity will be four times the wave velocity if