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In the arrangement shown, end $A$ of light inextensible string is pulled up with constant velocity $v$. The velocity of block $B$ is

Find the reading of the spring balance for the system shown in the figure. The elevator is going up with an acceleration of $\frac{g}{10}m/s^2$.
(Take $g=10/s^2$)

A particle undergoes SHM of period T starting from mean position. The time taken in ${\frac{3}{8}}^{th}$ oscillation is

A cyclist turns around a curve at 15 miles/hour. If he turns at double the speed, the tendency to overturn is

The position of the particle is given by $x=t^2-6t$ in $\text{m}$. The average speed of the particle in $4\text{sec}$ is

Source and observer start moving simultaneously along x and y-axis, respectively. The speed of source is twice the speed of observer, V₀. If the ratio of observed frequency to the frequency of the source is 0.75, find the velocity of sound.

The acceleration of a body due to the attraction of the earth (radius R) at a distance 2R from the surface of the earth is (g = acceleration due to gravity at the surface of the earth)

In the figure shown the acceleration of $A$ is ${\overrightarrow{a}}_A=15\hat{i}+15\hat{j}$, then the acceleration of $B$ is ($A$ remains in contact with $B$ ).

A U-tube with both end open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of $10mm$ above the water level on the other side. Meanwhile the water rises by $65mm$ from its original level (see diagram). The density of the oil is

A ring of mass $M$ and radius $R$ is rotating with angular speed about a fixed vertical axis passing through its centre $O$ with two point masses each of mass $\frac{M}{8}$ at rest at $O$. These masses can move radially outwards along two massless rods fixed on the ring as shown in the figure. At some instant the angular speed of system is $\frac{8}{9}\omega$ and one of the masses is at a distance of $\frac{3}{5}R$ from $O$. At this instant the distance of the other mass from $O$ is

Protons having kinetic energy K emerge from an accelerator as a narrow beam. The beam is bent by a perpendicular magnetic field so that it just misses a plane target kept at a distance l in front of the accelerator. Find the magnetic field.

A zener diode having breakdown voltage equal to $15V$, is in a voltage regulator circuit as shown in figure. The current through the diode is

A man is siting on the shore of a river. He is in the line of a 1.0 m long boat and is 5.5 m away from the centre of the boat. He wishes to throw an apple into the boat. If he can throw the apple only with a speed of 10 m/s, find the minimum and maximum angles of projection for seccessful shot. Assume that the point of projection and the edge of the boat are in the same horizontal level.

The resistance per unit length of a wire is ${10}^{-6}\Omega /m$. It is bent in the form of a circle of diameter 2 m. A wire of same material and cross sectional area is connected across its diameter. The total resistance across its diameter $AB$ will be

A boy throws a water-filled balloon at an angle of ${53}^{\circ }$ with a speed of $10m/s$. A car is advancing towards the boy at a constant speed of $5m/s$. If the balloon is to hit the car, how far away should the car be when the balloon is thrown? $(g=10m{s}^{-2})$

A capacitor of capacitance 1 μF is charged to a potential of 1 V. It is connected in parallel to an inductor of inductance 10^-3 H. The maximum current that will flow in the circuit has the value

What is the unit vector perpendicular to the following vectors 2$\hat{i}$ + 2$\hat{j}$ - $\hat{k}$ and 6$\hat{i}$ - 3$\hat{j}$ + 2$\hat{k}$

For the cell:

${Tl}_{\left(s\right)}$/${Tl}^{+}$ (0.001M)// ${Cu}^{+2}$(0.1M)/${Cu}_{\left(s\right)}$:

$E_{cell}$​ = 0.83V at 298K, The cell potential can be increased by

A space-ship is put into a circular orbit close to Earth's surface. What additional velocity must be imparted to the ship so that it is able to escape the gravitational pull of Earth(approximately)? $(R=6400km,g=9.8\frac{m}{s^2})$

A Pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now:

A spaceship of speed $v_0$ travelling along +y axis suddenly shots out one fourth of its part with speed $2v_0$ along + x – axis. x,y axes are fixed with respect to ground. The velocity of the remaining part is:

If at $t=0$, a travelling wave pulse on a string is described by the function $Y=\frac{6}{x^2+3}$. What will be the wave function representing the pulse at time t, if the pulse is propagating along positive x-axis with speed $4m/s$?

Differentiation of the function $y=2\tan x+x^4$ is +.

The bob of a pendulum at rest is given a sharp hit to impact a horizontal velocity $\sqrt{3.5gl}$, where $l$ is the length of the pendulum. Find the height at which tension in the string is zero.

A Carnot's engine is made to work between $227{}^{\circ }C$ and $27{}^{\circ }C$ first and then between $27{}^{\circ }C$ and $-173{}^{\circ }C$. The ratio of efficiency of second process to first process $\left(\frac{{\eta }_2}{{\eta }_1}\right)$ of the engine in the two cases is

Let ${\nu }_1$ be the frequency of the series limit of the Lyman series, ${\nu }_2$ be the frequency of the first line of the Lyman series, and ${\nu }_3$ be the frequency of the series limit of the Balmer series, then

A plane passes through (2,3, -1) and is perpendicular to the line having direction ratios 3, -4, 7 The perpendicular distance from the origin to this plane is

Two persons are holding a rope of negligible weight tightly at its ends so that it is horizontal. A 15kg weight is attached to the rope at the mid-point. The minimum tension required to completely straighten the rope is

In the circuit shown in figure, $X$ is joined to $Y$ for a long time and then $X$ is joined to $Z$. The total heat produced in $R_2$ is

A ball is suspended from the top of a cart by a light string of length $1.0$ m. The cart and the ball are initially moving to the right at constant speed V, as shown in figure (1). The cart comes to rest after colliding and sticking to a fixed bumper, as in figure (2). The suspended ball swings through a maximum angle ${60}^{\circ }$. The initial speed V is (neglect friction and take $g=10m/s^2$)

Two blocks of masses 3kg and 6kg are connected by a light spring and placed on a smooth horizontal surface. Initially, the spring is unstretched and the 3kg block is given a velocity of 2m/s to the left as shown in the figure. Find the maximum velocity of 6kg block

Find velocity of ring B ($V_B$) at an instant as shown. The string is taut and inextensible:

Consider two concentric spherical shells of radius R and 2R; with same surface charge density. If total charge on them is Q, then find electric potential at their centre.

The instantaneous oscillating electric field of EM wave is $E_0\hat{j}$ and magnetic field is oscillating along -ve $\left(\hat{k}\right)$ direction having magnitude $B_0$, then velocity of EM wave is

The dominant mechanisms for the motion of charge carriers in forward and reverse biased germanium p-n junctions are :

A point traversed half of the distance with a velocity $v_0$. The remaining part of the distance was covered with velocity $v_1$ for half the time and with velocity $v_2$ for the other half of the time. The mean velocity of the point averaged over the whole time of motion is

A force of 100 N needs to be applied parallel to a smooth inclined plane just to hold a body on it. The angle of inclination of the inclined plane is ${30}^o$. How much horizontal force need to be applied to do the same?

A particle moves from position, ${\overrightarrow{r}}_1=3\hat{i}+2\hat{j}-6\hat{k}$ to position ${\overrightarrow{r}}_2=14\hat{i}+13\hat{j}-9\hat{k}$ under the action of force $(4\hat{i}+\hat{j}+3\hat{k})$ $\text{N}$. Calculate the work done.

A heavy but uniform rope of length $L$ is suspended from a ceiling. A particle is dropped from the ceiling. At the same instant, the bottom end is given a jerk. Find the velocity of wave pulse at an instant when particle and pulse are at same level.

A body is traveling down an inclined plane of angle of ${30}^{\circ }$ with an acceleration of $2m/s^2$, leaves it with speed of $20m/s$. If the inclined plane is located at a certain height above the ground, find its velocity when it travels in the horizontal direction after $1\text{second}$.

What are internal and external forces?

Two particles of equal masses moving with same speed collide perfectly in-elastically. After the collision, the combined mass moves with half of the speed of the individual masses. The angle between the initial momenta of individual particle is .

Why isthe electric potential energy of 2 +ve particles separated by some distance 0?