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Find the density of the oil inside the U-tube as shown in figure. (Take density of water ${\rho }_w=1000{\text{kg/m}}^3$)

Two point charges $-4\mu C$ and $+4\mu C$ are placed at points A$(1,0,4)$ and B$(2,-1,5)$ located in an electric field $\overrightarrow{E}=0.20\hat{i}V/cm$ . The magnitude of torque acting on the dipole is

The liquid meniscus in capillary tube will be convex, if the angle of contact is

A truck is moving with a constant velocity of $54\text{km/h}$. In which direction (angle with the direction of motion of truck) should a stone be projected up with a velocity of $20\text{m/s}$ relative to truck, so that for a person standing on the earth stone appears to be at right angles to the truck ?

A particle (A) is dropped from a height and another particle (B) is thrown in horizontal direction with speed of 5 m/sec from the same height, bith occuring at the same time. The correct statement is

A wire $X$ of half the diameter and half the length as of a wire $Y$ of similar material. The ratio of resistances of $X$ to that of $Y$ is -

The coefficient of volume expansion of glycerin is $49\times {10}^{-5}{{}^{\circ }\text{C}}^{-1}$. The fractional change in the density on a $30{}^{\circ }\text{C}$ rise in temperature is

In the figure shown the velocity of lift is 2 m/s while string is winding on the motor shaft with velocity 2 m/s and block A is moving downwards with velocity of 2 m/s, the find out the velocity of block B.

A bomber plane moves horizontally with a speed of 500 m/s and a bomb released from it, strikes the ground in 10 sec. Angle with the horizontal at which it strikes the ground will be (g=10 m/$s^2$)

1. 1.5

A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hands of a person standing in the car. The car is moving with constant acceleration $a$ directed horizontally as shown in figure. The other end of the string is pulled with constant acceleration $a$ vertically. The tension in the string is equal is

Consider Fraunhofer diffraction pattern obtained with a single slit illuminated at normal incidence. At the angular position of the first diffraction minimum, the phase difference (in radius) between the wavelets from the opposite edge of the slit is:

1. 4

A disc of radius R and mass M is pivoted at the rim and is set for small oscillations. If simple pendulum has to have the same period as that of the disc, the length of the simple pendulum should be

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides, as shown in the figure. The radius of vessel is $5\text{cm}$ and the angular speed of rotation is $\omega {\text{rad s}}^{–1}$. The difference in the height, $h\text{(in cm)}$ of liquid at the centre of the vessel and at the side will be :

The electric field of a radio wave is given by $\overrightarrow{E}=E_0\sin (kz-\omega t)(\hat{i}+\hat{j}).$ Give a unit vector in the direction of the magnetic field at a place and time where $\sin (kz-\omega t)$ is positive.

A uniformly charged ring with radius $0.5\text{m}$ has $0.002\pi \text{m}$ gap. If the ring carries a charge of $+1\text{C}$, the electric field at the centre is

A $4.0\text{kg}$ mass sliding on a frictionless horizontal surface explodes into two equal parts, one moving with $3.0\text{m/s}$ due north and the other with $5.0\text{m/s}$ due ${30}^{\circ }$ north of east. What is the original speed of the mass?

Five facts about real signal x(t) with Laplace transform X(s) are given below :



1. X(s) has exactly two poles.

2.X(s) has no zeros in the finite s-plane.

3. X(s) has a pole at s = -1 + j.

4. $e^{2t}x\left(t\right)$ is not absolutely integrable.

5. X(0) = 8.

A long insulated copper wire is closely wound as a spiral of ‘N’ turns. The spiral has inner radius ‘a’ and outer radius ‘b’. The spiral lies in the XY plane and a steady current ‘I’ flows through the wire. The Z-component of the magnetic field at the centre of the spiral is :

A capacitor is charged by using a battery which is then disconnected. A dielectric slab is then slipped between the plates, which results in

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two unit vectors, then $\overrightarrow{a}\times \overrightarrow{b}$ will also be a unit vector if:

In the figure shown all the surface are smooth. All the blocks A, B and C are movable, positive x-axis is horizontal and positive y-axis vertical as shown. Just after the system is released from the position as shown.

A
non-uniform bar of weight W
is
suspended at rest by two strings of negligible weight as shown in
Fig.7.39. The angles made by the strings with the vertical are 36.9°
and 53.1° respectively. The bar is 2 m long. Calculate the
distance d
of the
centre of gravity of the bar from its left end.

A capacitor charged to $50\text{V}$ is discharged by connecting the two plates. The connections are made at $t=0$. At $t=10\text{ms}$, the potential difference across the plates is found to be $1.0\text{V}$. Find the potential difference at $t=20\text{ms}$.

A system consists of two small spheres of mass $1\text{kg}$ and $2\text{kg}$ interconnected by a weightless spring. At $t=0$, the spheres are set in motion with initial velocities as shown in the figure. The position vector of centre of mass at $t=0$ is $\left(20\hat{j}\right)\text{m}$. Initially, spring is in its natural length. The system moves in earth's gravitational field. The position vector of centre of mass of the system in $\text{m}$ at $t=1\text{s}$ is



$[g=10{\text{m/s}}^2,\text{com is initial centre of mass}]$