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A truck moving on a smooth horizontal surface with a uniform speed 'u' is carrying stone-dust. If a mass $\Delta m$ of the stone-dust `leaks down’ from the truck in the time $\Delta t$, the force needed to keep the truck moving at its uniform speed is

What is the SI unit of
mass? How is it defined?

One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown in the figure,





The change in internal energy of the gas during the transition is:

A person throws vertically $n$ balls per second with the same velocity. He throws a ball whenever the previous one is at its highest point. The height to which the balls rise is

Two coherent narrow slits emitting sound of wavelength $\lambda$, in the same phase are placed parallel to each other at a small separation of $2\lambda$. The sound is detected by moving a detector on the screen which is placed at a distance $d$ from the slit $S_1$ as shown in figure. Find the distance $y$ such that the intensity at $P$ is equal to intensity at point $O$ if $d>>\lambda$.

A car travels from A to B at a speed of 20 km/hr and returns at a speed of 30 km/hr. The average speed of the car for the whole journey is

When source and detector are stationary but the wind is blowing at speed , the apparent wavelength ${\lambda }^{\prime }$ on the wind side is related to actual wavelength $\lambda$ by [take speed of sound in air as v]

A simple pendulum of bob of mass $m$ and length $l$ has one of its ends fixed at the centre $O$ of a vertical circle, as shown in the figure. If $\theta ={60}^{\circ }$ at the point P, the minimum speed $u$ that should be given to the bob so that it completes a vertical circle is

If a particle has velocity $v\left(t\right)=t^2-7t+12$, the average speed in $6\text{sec}$ is

A ball is released from the top of tower of height $h$ meter. It takes $T$ second to reach the ground. What is the position in $\text{(m)}$ from the ground of the ball in $\frac{T}{3}$ second?

If a thermometer on $C-$scale reads freezing point of water as $20C$ and boiling point as $150C$, how much the thermometer would read when the actual temperature is ${60}^{\circ }\text{C}$?

A double slit $S_1-S_2$ is illuminated by a coherent ight of wavelength \lambda the slits are separated by a distance d. A plane mirror is placed in front of the double slit at a distance $D_1$ from it and a screen $\sum$ is placed behind the double slit at a distance $D_2$ from it (figure 17 - E2). The screen $\sum$ receives only the light reflected by the mirror. Find the fringe -width fo te interference pattern on the screen.

A light ray, going through a prism with the angle of prism ${60}^{\circ }$, is found to deviate by ${30}^{\circ }$. What limit on the refractive index can be put from these data ?

A glass sinker has a mass $M$ in the air. When weighed in a liquid at temperature $t_1$, the apparent mass is $M_1$ and when weighed in the same liquid at temperature $t_2$, the apparent mass is $M_2$. If the coefficient of cubical expansion of the glass is ${\gamma }_g$, then coefficient of expansion of the liquid is

What is the angle between two forces of equal magnitude such that the resultant is one-third as much as either of the original forces?

Calculate the bulk modulus of air from the following data about a sound wave of wavelength 35 cm travelling in air. The pressure at a point varies between $(1.0\times {10}^5\pm 14)$ Pa and the particles of the air vibrate in simple harmonic motion of amplitude $5.5\times {10}^{-6}m$.

A rectangular loop with a sliding connector of length $10cm$ is situated in uniform magnetic field perpendicular to plane of loop. The magnetic induction is $0.1$ tesla and resistance of connector $\left(R\right)$ is $1$ ohm. The sides $AB$ and $CD$ have resistances $2$ ohm and $3$ ohm respectively. Find the current in the connector during its motion with constant velocity $1m/s$.

The pressure in the tyre of a car is four times the atmospheric pressure at $300K$. If this tyre suddenly brusts, its new temperature will be :
$(\gamma =1.4)$

A simple pendulum has a time period $T$ in vaccum. Its time period when it is completely immersed in a liquid of density one-eight of the density of material of the bob is

The capillary action for various liquid-solid pairs is given below.
Match the correct meniscus, angle of contact and what happens to the level of liquid.

$\begin{array}{ccc}& & \\ \text{Meniscus}& \text{Angle of contact}& \text{Level}\\ \text{(A) Concave}& \left(i\right)\theta >{90}^{\circ }& \left(a\right)\text{Fall}\\ \text{(B) Plane}& \left(ii\right)\theta <{90}^{\circ }& \left(b\right)\text{No rise or fall}\\ \text{(C)Convex}& \left(iii\right)\theta ={90}^{\circ }& \left(c\right)\text{Rise}\end{array}$

A bat emits ultrasonic sound of frequency $100\text{kHz}$ in air. If the sound gets reflected (without transmission and loss of energy) from a water surface then wavelength of the reflected sound is
[speed of sound in air is $340{\text{ms}}^{-1}$]

A small ball 'A' of mass 'm' is attached rigidly to the end of a light rod of length 'd'. The structure rotates about an axis perpendicular to the rod and passing through its other end with an angular velocity '$\omega$'. The angular momentum of the system about this axis is.

Three particles A, B and C are situated at the vertices of an equilateral triangle ABC of side 'd' at t = 0. Each of the particles moves with constant speed v. A always has its velocity along AB, B along BC and C along CA. At what time will the particles meet each other?

Maximum and minimum values of the resultant of two forces acting at a point are 7 Newton and 3 Newton respectively the smaller force will be equal to

A particle is projected upwards with a velocity of 100 m/s at an angle of 60°, with the vertical.
Then time taken by the particle when it will move perpendicular to its initial direction. Please explain and give answer.

An alternating current (in ampere) varies with time t as $I=3sin\omega t+4cos\omega t$. The rms value of the current is

At what distance should two charges, each equal to 1 C, be placed so that the force between them equals your weight?

Displacement of a particle is given by the expression x=2t² -12t-9, where x is in meter and t is in seconds. What is acceleration and max velocity?

At $STP$ the order of mean square velocity of molecules of $H_2,N_2,O_2$ and $HBr$ is-

The simple pendulum bob is given a horizontal velocity $\sqrt{gl}$ at the bottom. The angle with the vertical through which the ball swings before its velocity becomes zero is

The number of particles crossing a unit cross-sectional area perpendicular to $x-$axis in unit time is given by $n=-D\left(\frac{n_2-n_1}{x_2-x_1}\right)$, where $n_1$ and $n_2$ are the number of particles per unit volume crossing a cross-sectional area at distances $x_2$ and $x_1$. Find the dimension of diffusion constant $D$.

In an experiment to measure the speed of conduction of a nerve impulse along a giant axon, the distance between the stimulating and recording electrodes was varied and the delay between stimulus and response was recorded for each distance. The results are shown in the graph below:


From these results the mean speed of conduction was found to be

A galvanometer having a coil resistance of 100$\Omega$ gives a full scale deflection, when a current of 1 mA is passed through it. The value of resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of 10 A, is:

If $\overrightarrow{a}=\hat{i}-\hat{j}$ and$\overrightarrow{b}=3\hat{i}+4\hat{j}$, the vector having the same magnitude as $\overrightarrow{b}$ and parallel to $\overrightarrow{a}$ is

Conservative and nonconservative forces

Two small bodies of masses 10 kg and 20 kg are kept a distance 1.0 m apart and released, assuming that only mutual gravitational forces are acting find the speeds of the particles when the separation decreases to 0.5 m.

A non-planar loop of conducting wire carrying a current I is placed as shown in the figure. Each of the straight sections of the loop is of length 2a. The magnetic field due to this loop at the point P (a,0,a) is in the direction of