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A body weighs 450 gf in air and 310 gf when completely immersed in water. Find :
(i) the volume of the body,
(ii) the loss in weight of the body, and
(iii) the upthrust on the body. State the assumption made in part (i).

Two metallic spheres of radii $2\text{cm}$ and $6\text{cm}$ are given charge $3\times {10}^{-2}\text{C}$ and $7\times {10}^{-2}\text{C}$, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is :

If velocity is given as $v=\alpha -\beta x$, then dimensional formula of $\beta {\alpha }^2$ is

Work done by a conservative force on a system is equal to

If the heat of $110\text{J}$ is added to a gaseous system and it acquires internal energy of $40\text{J}$, then the amount of internal work done is

If a negative charge is kept at point $\text{P}$ in the electric field of two charges then it will initially accelerate along

A particle moves with deceleration along the circle of radius $R$ so that at any moment of time its tangential and normal accelerations are equal in moduli. At the initial moment $t=0$ the speed of the particle equals $v_0$, then the speed of the particle as a function of the distance covered $S$ will be

A block of mass $m$ is placed on another block of mass $M$ which itself is lying on a horizontal surface. The coefficient of friction between two blocks is ${\mu }_1$ and that between the block of mass $M$ and horizontal surface is ${\mu }_2$. What maximum horizontal force can be applied to the lower block so that the two blocks move without separation?

An increase in intensity level of 1 dB implies an increase in intensity of (given anti $lo{g}_{10}0.1=1.2589)$

A cylindrical object of outer diameter 10 cm, height 20 cm and density 8000 kg $m^{-3}$ is supported by a vertical spring and is half dipped in water as shown in figure. (a) Find the elongation of the spring in equilibrium condition. (b) If the object is slightly depressed and released, find the time period of resulting oscillations of the object. The spring constant = 500 N $m^{-1}$

As shown in the figure a metal rod makes contact and complete the circuit. The circuit is perpendicular to the magnetic field with B=0.15 tesla If the resistance is $3\Omega$ , force needed to move the rod as indicated with a constant speed of 2m/sec is

A solid metallic sphere of radius r is charged to a voltage V. It is enclosed by a thin spherical shell of radius 2r. If q is the charge on the sphere and the shell each, the potential difference between them will be $\frac{xV}{2}$. What is x?

A block of mass $0.1\text{kg}$ is held against a wall applying a horizontal force of $5\text{N}$ on the block. If the coefficient of friction between the block and the wall is $0.5$, the magnitude of the frictional force acting the block is

For a particle moving along $x$ - axis, the acceleration $a$ of the particle in terms of its $x$ - coordinate is given by $a=-9x$, where $x$ is in meters and $a$ is in ${\text{m/s}}^2$. Take acceleration, velocity and displacement in positive $x$ - direction as positive. The initial velocity of particle at $x=0$ is $u=+6\text{m/s}$. The maximum distance of the particle along the positive $x$-direction from origin will be

An automobile negotiates a turn of radius $\frac{40}{\sqrt{3}}\text{m}$ on a road which is banked at the curve at angle ${30}^{\circ }$ to the horizontal. If coefficient of friction between road surface and automobile is $\frac{1}{\sqrt{3}}$ then maximum speed at which the car can negotiate the turn without skidding will be $(g=10{\text{m/s}}^2)$

The temperature of equal masses of three different liquids $A$, $B$, $C$ are ${12}^{\circ }C$, ${19}^{\circ }C$ and ${28}^{\circ }C$ respectively. The temperature when $A$ and $B$ are mixed is ${16}^{\circ }C$ while when $B$ and $C$ are mixed, it is ${23}^{\circ }C$. What would be the temperature when $A$ and $C$ are mixed?

Calculate the separation of two points on moon that can be resolved using $600\text{cm}$ telescope. Given distance of moon from earth, $=3.8\times {10}^{10}\text{cm}$. The wavelength most sensitive to eye is $5.5\times {10}^{-5}\text{cm}$.

Two vectors have magnitudes $3$ units and $4$ units respectively. What should be the angle between them if the magnitude of the resultant is $5$ units?

An object is released from some height. Exactly after one second, another object is released from the same height. The distance between the two objects exactly after $2$ seconds of the release of second object will be

Two bodies of different masses $m_a$ and $m_b$ are dropped from two different height $a$ and $b$. The ratio of the time taken by the two to cover these distances are

Two fixed frictionless inclined plane making an angle ${30}^{\circ }$ and ${60}^{\circ }$ with the vertical are shown in the figure. Two blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B?

Sand is pouring from
a pipe at the rate of 12 cm³/s.
The falling sand forms a cone on the ground in such a way that the
height of the cone is always one-sixth of the radius of the base. How
fast is the height of the sand cone increasing when the height is 4
cm?

Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli’s equation? Explain.

According to Newton's third law each team pulls the opposite team with equal force in a game of tug of war. Why then does one team win and the other lose?

Two blocks of equal masses $m_1=m_2=3kg$, connected by a light string, are placed on a horizontal surface which is not frictionless. If a force of 20 N is applied in the horizontal direction on a block, the acceleration of each block is $0.5m{s}^{-2}$. Assuming that the frictional forces on the two blocks are equal, the tension in the string will be

A magnetic dipole of dipole moment $M=10{\text{Am}}^2$ is suspended at angle ${45}^{\circ }$ in an external magnetic field of $\sqrt{2}\times {10}^{-5}\text{T}$. Find the work done by the magnetic field to bring the dipole moment to be in stable equilibrium ?

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 -

A horizontal wind is blowing with a velocity $v$ towards north-east. A man starts running towards north with acceleration $a$. The time after which man will feel the wind blowing towards east is

If the length of a pendulum is made 9 times and mass of the bob is made 4 times then the value of time period becomes

The total revenue in rupees received from the sale of x units of a product is given by $R\left(x\right)=3x^2+36x+5$. The marginal revenue, when x=15 is

a) 116

b) 96

c) 90

d) 126