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A curve between magnetic moment and temperature of magnet is

A source of sound 'S' emitting waves of frequency $100Hz$ and an observer 'O' are located at some distance from each other. The source is moving with a speed of $19.4m{s}^{-1}$ at an angle of ${60}^o$ with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer is
(velocity of sound in air $330m{s}^{-1}$)

A voltage of peak value $283\text{V}$ and varying frequency is applied to a series $L-C-R$ combination in which $R=3\Omega ;L=25\text{mH}$ and $C=400\mu F$. Then, the frequency (in $Hz$) of the source at which maximum power is dissipated in the above, is

Two non-mixing liquids of densities $\rho$ and $n\rho (n>1)$ are put in a container. The height of each liquid is $h$. A solid cylinder of length $L$ and density $d$ is put in this container. The cylinder floats with its axis vertical and length $pL(p<1)$ in the denser liquid. The density $d$ is equal to:

Radius of gyration of a body about an axis$\left(I_A\right)$ is $5\text{m}$. Perpendicular distance of $\left(I_A\right)$ from center of mass of body is $3\text{m}$. Find its radius of gyration about an axis$\left(I_B\right)$ which is parallel to $\left(I_A\right)$ and also passing through center of mass of body.

A particle of mass $m$ just completes the vertical circular motion. What will be the difference in tension at the lowest and highest point?

A body of mass $m$ hangs by as inextensible light string that passes over a smooth massless pulley that is fitted with a light spring of stiffness $k$ as shown in the figure. If the body is released from rest, calculate the maximum elongation of the spring. Take $g=10{\text{m/s}}^2$.

A car has an initial velocity of $100\text{m/s}$. On the application of brakes the car stops at $200\text{m}$. The acceleration of the car will be

Three particles each of mass $1\text{kg}$ are placed at the vertices of an equilateral triangle $ABC$ of side $2\text{m}$. Find the moment of inertia of system about a line perpendicular to the plane of system and passing through middle point ($D$) of side $BC$ of the triangle.

Assuming that the surface is frictionless and strings are inextensible, find the acceleration of the block of mass $2m$ shown in the figure.

An ideal transformer has $500$ primary turns and $10$ secondary turns. The primary coil carries current $2A$ and its voltage is $11,000V$. Current and voltage in the secondary coil will be

At constant volume, when the temperature of a gas increases by $1^{\circ }\text{C}$, its pressure increases by $0.4\%$. What is its initial temperature ?

Find the minimum value of force $F$ for which the system remains at rest. Take $g=10m/s^2$.

A car starts from rest. It has to cover a distance of $500\text{m}$ and come to rest at the end of the journey. The coefficient of friction between the road and the tyre is $\frac{1}{2}$. The minimum time in which the car can cover this distance is $(g=10{\text{m/s}}^2)$

What is Lenz's law?

Two rotating bodies, $A$ and $B$ with moments of inertia $I_A$ and $I_B(I_B>I_A)$ about the same axis have equal rotational kinetic energy. If $L_A$ and $L_B$ be their angular momentum respectively then

A 110V DC heater is used on an AC source such that the heat produced is same as it produces when connected to 110V DC in same time interval. What would be the RMS value of alternating voltage?

A)110V

B)220V

C)330V

D)440V

Question 06

Which of the following properties of atom could be explained correctly by Thomson model of atom ?

(a) Overall neutrality of atom

(b) Spectra of hydrogen atom

(c) Posittion of elecrtons, protons and neutrons in atom

(d) Stabilityof atom

A spring - block pendulum is shown in the figure. The system is hanging in equilibrium. A bullet of mass m/2 moving with a speed u hits the block from down and gets embedded as shown in the figure. Find the amplitude of oscillation now.

Two balls are projected from point A and B in vertical plane as shown. The balls can collide in mid air if $v_1/v_2$ is equal to

A body of mass ${}^{\prime }{m}^{\prime }$ hangs from three springs, each of spring constant ${}^{\prime }{k}^{\prime }$ as shown in the figure. If the mass is slightly displaced and let go, the system will oscillate with time period

The equation of a stationary and a travelling waves are $y_1=a\sin kx\cos \omega t$ and $y_2=a\sin (\omega t-kx)$ respectively. The phase difference between two points, $x_1=\frac{\pi }{3k}$ and $x_2=\frac{3\pi }{2k}$ is ${\varphi }_1$ in the standing wave $y_1$ and is ${\varphi }_2$ in travelling wave $y_2$ then the ratio $\frac{{\varphi }_1}{{\varphi }_2}$ is

A wire has a resistance of 6$\Omega$. It is cut into two parts and both half values are connected in parallel. The new resistance is

If a spring extends by $x$ on loading, then energy stored by the spring is (Given: $T$ is the tension in spring and $k$ is spring constant)

A stone of mass m is tied to a string and is moved in a vertical circle of radius R making f revolutions per minute. The total tension in the string when the stone is at its lowest point is

Wires 1 and 2 carrying currents $i_1$ and $i_2$ respectively are inclined at an angle $\theta$ to each other. The force on a small element ‘dl’ of wire 2 at a distance ‘n’ from the wire 1, as shown in figure, due to the magnetic field of wire 1 is

Projection of $\overrightarrow{A}$ along the vector $\overrightarrow{B}$ is

Assuming the string to be inextensible and surface and pulley to be frictionless, velocity of block $B$ $\left(V_B\right)$ in the given figure is

The velocity of a bullet is reduced from $200\text{m/s}$ to $100\text{m/s}$ while travelling through a wooden block of thickness $10\text{cm}$. The retardation, assuming it to be uniform, will be

In the figure shown, a hole of radius $2\text{cm}$ is made in a semicircular disc of radius $6\pi$ at a distance $8\text{cm}$ from the centre $\text{C}$ of the disc. The distance of the centre of mass of this system from point $\text{C}$ is: (COM of semicircle of radius $r$ is at distance $\frac{4r}{3\pi }$ from the base)

In the given arrangement, find the distance travelled by wedge $B$ in $1sec$. System starts from rest. $(\theta ={60}^{\circ })$

A hanging body of mass $m_1$ is pulled by a force F = $m_2$ g acting on the massless inextensible smooth string. The acceleration of $m_1$ is:

A $1\text{kg}$ particle strikes a wall with a velocity $1\text{m/s}$ at an angle ${30}^{\circ }$ and reflects at the same angle in $0.1$ second, then the force applied by the wall on the particle will be

Find $F$ such that the $2\text{kg}$ body goes up with an acceleration of $2{\text{m/s}}^2$.
Take ($g=10{\text{m/s}}^2$)

If the coefficient of friction between A and B is $\mu$, the maximum acceleration of the wedge A for which B will remain at rest with respect to wedge is

A projectile is given an initial velocity of $\hat{i}+2\hat{j}$. The Cartesian equation of its path is
$(\text{Take}g=10m/s^2)$

A circular coil of radius 4 cm and of 20 turns carries a current of 3 amperes. It is placed in a magnetic field of intensity of 0.5 . The magnetic dipole moment of the coil is

Assertion : If dot product and cross product of vector A and vector B are zero, it implies that one of the vector A and B must be a null vector.

Reason : Null vector is a vector with zero magnitude.

Straight distance between a hotel and a railway station is 10 kms but circular route is followed by a taxi covering 23 kms in 28 mins. What is the average speed and magnitude of average velocity? Are they equal?

A rod of length $10\text{cm}$ made up of conducting and non-conducting material (shaded part is non-conducting). The rod is rotated with constant angular velocity $10\text{rad/s}$ about point $O$, in constant magnetic field of $2T$ as shown in the figure. The induced emf between the point $A$ and $B$ of rod will be:

By sucking through a straw, a student can reduce the pressure in his lungs to $750\text{mm}$ of $Hg$ (density $=13.6{\text{gm/cm}}^3$). Using the straw, he can drink water from a glass upto a maximum depth of :

A mixture of $4\text{g}$ of hydrogen and $8\text{g}$ of helium at pressure $P=1.01\times {10}^5\text{Pa}$ and temperature $T=273\text{K}$ has a density of about

If $U_1,U_2,U_3$ represent the potential energy differences for moving a particle from $A$ to $B$ along three different paths $1,2\&3$ (as shown in the figure) in the gravitational field of point mass $m$, find the correct relation between $U_1,U_2\&U_3$.

Which of the following relations is wrong?