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The arrangement of pulley-block system is released from rest at $t=0$ as shown in figure. The velocity of block $B$ is $v_B=45\text{m/s}$ upwards at some instant. Then, find the magnitude of velocity of block $A$ in $\text{m/s}$. Consider the string to be massless and inextensible, all pulleys are light and smooth.

The volumes of two vessels are $5\text{litre}$ and $3\text{litre}$ respectively. Air is filled in them at pressure of $3$ atm and $5$ atm respectively. At constant temperature if they are connected through a tube, the resultant pressure will be

The equivalent resistance between the points $A$ and $B$ in the circuit shown in the following figure is

Fig. Shows a plot of the conservation force F in a unidimensional field. The plot representing the function corresponding to the potential energy (U) in the fields is

A body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragments with equal masses fly in mutually perpendicular directions with speeds of 21 m/s. The velocity of the heaviest fragment will be

If if the distance travelled by the body in the nth second is given by (4 + 6n) then find the initial velocity and acceleration of the body

The state of an ideal gas is changed through an isothermal process at temperature $T_o$ as shown in figure. The work done by the gas going from state $B$ to $C$ is double the work done by gas in going from state $A$ to $B$. If the pressure in the state $B$ is $\frac{P_o}{2}$, then the pressure of the gas in state $C$ is

If $I_n=\int \frac{t^n}{1+t^2}dt,$ then $I_6+I_4=$

(where $C$ is integration constant)

Two forces, each of magnitude F have a resultant of the same magnitude F. The angle between the two forces is

A hollow smooth uniform sphere $A$ of mass ${}^{\prime }{m}^{\prime }$ rolls without sliding on a smooth horizontal surface. It collides elastically and head on with another stationary smooth solid sphere $B$ of the same mass $m$ and same radius. The ratio of kinetic energy of ${}^{\prime }{B}^{\prime }$ to that of ${}^{\prime }{A}^{\prime }$ just after the collision is

Two long strings $\text{A}$ and $\text{B}$ each having linear mass density $1.2\times {10}^{-2}\text{kg/m}$ are stretched by different tensions $4.8\text{N}$ and $7.5\text{N}$ respectively and are kept parallel to each other with their left ends at $x=0$. Wave pulses are produced on the string at the left ends at $t=0$ on string$\text{A}$ and $t=20\text{ms}$ on string $\text{B}$. When will the pulse on $\text{B}$ overtake that on $\text{A}$ for the first time?

A balloon was moving upwards with a uniform velocity of $10{\text{ms}}^{-1}$. An object of finite mass is dropped from the balloon when it was at a height of $75\text{m}$ from the ground level. The height of the balloon from the ground when the object strikes the ground will be around :

$(\text{Take}g=10{\text{ms}}^{-2})$

Consider a car of mass $1000\text{kg}$ moving with a speed of $36\text{km/h}$ on a smooth road and colliding with a horizontally mounted spring of spring constant $10{\text{KNm}}^{-1}$. Find the maximum compression of the spring.

The value of g (acceleration due to gravity) at earth's surface is 10 ms^{​​​​​-2} its value in ms^{​​​​​-2} at centre of earth which is assumed to be a sphere of radius R metre and uniform mass density is

A hollow cylindrical shell of radius $R=0.1\text{m}$ has mass $M=6\text{kg}$. It is filled with water having mass $m=3\text{kg}$. It is placed on an inclined plane connected to a spring of spring constant $k=15\text{N/m}$ as shown in the figure. When it is disturbed, it performs oscillations without slipping on the inclined plane. The frequency of the resulting oscillations is

[Assume that the liquid does not rotate inside the cylindrical shell]

An object of weight W and density $\rho$ is dipped in a fluid of density ${\rho }_1$. Its apparent weight will be

Consider a circular coil of wire carrying current $I$, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by ${\varphi }_i$. The magnetic flux through the area of the circular coil area is given by ${\varphi }_0$. Which of the following option is correct?

In a beyblade game, the beyblade has an initial angular speed of $180\text{rpm}$. It slows down and eventually comes to rest in a time of 5 minutes. The average angular acceleration of the beyblade is

A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12 cm below the surface of water, the radius of the circle in centimetre is

A uniformly thick wheel, with moment of inertia $I$ and radius $R$, is free to rotate about its centre of mass (see fig.). A massless string is wrapped over its rim and two blocks of masses $m_1$ and $m_2>m_2$ are attached to the ends of the string. The system is released from rest. The angular speed of the wheel, when $m_1$ descents through a distance $h$, is

Twelve capacitors each having a capacitance $C$, are connected to form a cube. Find the equivalent capacitance of the cube along the face diagonal?

[Take $C=9\mu \text{F}$]

Two blocks of masses $m_A=10\text{kg}$ and $m_B=15\text{kg}$ initially moving in the same direction with velocities of $u_A=3\text{m/s}$ and $u_B=6\text{m/s}$ collide elastically. What is the velocity of the block of mass $10\text{kg}$ after the collision?

For the arrangement shown in the figure, $m_1=6\text{kg}$ and $m_2=4\text{kg}$. If the string is light and inextensible and the pulley and surfaces are frictionless, find the magnitude of the acceleration of the center of mass.
(Take $g=10m/s^2$)

A conducting circular loop of radius $2.2cm$ is placed in a uniform magnetic field of magnitude $0.04T$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $2mm/s$. The induced emf in the loop when the radius is $2cm$ is

The specific heat of an ideal gas is

A point charge $q$ is surrounded by eight fixed identical point charges at the same distance $r$ as shown in figure. How much work will be done by external force to remove point charge $q$ from centre $O$ to infinity very slowly?

Calculate the force with which you attract the earth.

Two polaroids are placed in the path of an unpolarized beam of light of intensity such that no light is emitted through the second polaroid. If now a third polaroid whose polarization axis makes an angle ${30}^{\circ }$ with polarization axis of the first is placed between these two polaroids, then the intensity of light emerging through the last polaroid will be