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A long cylindrical rod of radius $R_1$ is placed co-axially inside a cylindrical tube of radius $R_2(>R_1)$ filled withviscous liquid and pulled along the axis with a constant velocity. In steady state the velocity gradient $\left(\frac{dv}{dr}\right)$ depends on the distance from the common axis 'r' as proportional to

A watermelon seed has the following coordinates: x=-5.0 m, y=9.0 m and z=0 m. Find its position vector

(a) In unit-vector notation and as
(b) A magnitude and
(c) An angle relative to the positive direction of the x-axis

Two bodies of masses $1kg$ and $2kg$ are projected with same velocities, on two rough surfaces whose coefficients of friction are $0.2$ and $0.4$ respectively. Find the ratio of distances travelled by them before their velocities become half of the initial value.

A single-phase line consists of two long solid conductors, each having a radius of r metre separated by a distance of D metre. What will be the capacitance between the line

With the assumption of no slipping determine the mass $m$ of the block which must be placed on the top of a $5\text{kg}$ cart in order that the time period of oscillation is $2\text{sec}$. What is the minimum coefficient of static friction ${\mu }_s,$ for which the block will not slip relative to the cart, if the cart is displaced $300\text{mm},$ from the equilibrium position and released ?

At what time instance t, the particle's displacement is positive but particle's velocity negative

In the given constraint, if the pulley is frictionless and the string is inextensible, then velocity of block $B$ $\left(V_B\right)$ is

A force $F$ is acting on an object varies with distance $x$ is shown in the figure given below. The force is in $\text{N}$ and $x$ is in $\text{m}$. The work done by the force in moving the object from $x=0\text{to}x=6\text{m}$ is

The torque of the force $\overrightarrow{F}=\left(2\hat{i}-3\hat{j}+4\hat{k}\right)N$ acting at a point $\overrightarrow{r}=\left(3\hat{i}+2\hat{j}+3\hat{k}\right)m$ about the origin will be

A solid sphere of mass $M$ and radius $a$ is surrounded by a uniform concentric spherical shell of thickness $2a$ and mass $2M$. The gravitational field at distance $3a$ from the centre will be

At what ponts dipole field intensity is parallel to the line joining the charges?

The far point of a myopic person is 80cm . What is the power of the lens required to enable him to see very distant objects clearly?

A 50 turn closely wound circular coil of radius 12 cm carries a current of 2.4 A, the field at center of coil is.

Find the instantaneous axis of rotation of a rod of length $l$ from the end $A$ when it moves with a velocity $\overrightarrow{v_A}=v\hat{i}$ and the rod rotates with an angular velocity $\overrightarrow{\omega }=-\frac{v}{2l}\hat{k}$, shown in the figure.

If the distribution of molecular speeds of gas is as per the figure shown below, then the ratio of the most probable, the average, and the root mean square speeds, respectively, is:

Two ions having the same mass have charges in the ratio $1:2$. They are projected normally in a uniform magnetic field, with their speeds in the ratio $2:3$. The ratio of the radii of their circular trajectories is :

The resolving power of an electron microscope operated at $16\text{kV}$ is $R$. The resolving power of the electron microscope when operated at $4\text{kV}$ is

A sonometer wire is vibrating with a frequency of $30\text{Hz}$ in the fundamental mode. If the length of the wire is increased by $20\%$, the change in the frequency of the fundamental mode is

Why a moving charge contain magnitic field and how in detail

Two trains $P$ and $Q$ are moving along parallel tracks with same uniform speed of $\frac{20m}{s}$. The driver of train $P$ decides to overtake train $Q$ and accelerates his train by $\frac{1m}{s^2}$. After $50s,$ train $p$ crosses the engine of train $Q$. Find out what was the distance between the two trains initially provided the length of each train is $400m.$

The volume of a metal sphere increases by $0.15\%,$ when its temperature is raised by ${24}^{\circ }\text{C}$. The coefficient of linear expansion of metal is:

A point luminous object is placed at a distance of $30\text{cm}$ from the convex lens of focal length $20\text{cm}$ on the other side of the lens. At what distance from the lens, a convex mirror of radius of curvature $10\text{cm}$ be placed in order to have an upright image of the object coincident with it?

A coil of resistance $300\Omega$ and inductance $1.0H$ is connected across an alternating voltage of peak value $300V$ of frequency $\frac{300}{2\pi }Hz.$ Calculate the peak potential difference across inductor.

A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in the figure. If it starts its journey from rest at x = 0, its velocity at x = 12 m is