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If the radius of a sphere is measure as 7m with an error of 0.02 m, then find the approximate error in calculating its volume.

The acceleration of the particle moving in positive $x-$ direction with an initial velocity of $20\text{m/s}$ is $4{\text{m/s}}^2$. Its velocity at $t=5\text{sec}$ is

In the arrangement shown in figure, the relation between acceleration of blocks $m_1$ and $m_2$ is

A soap bubble is blown with the help of a mechanical pump at the mouth of a tube. The pump produces constant increase in the radius per minute of the bubble, irrespective of its internal pressure. The graph between the excess pressure $p$ inside the soap bubble and time $t$ will be

What is Angular Displacement?

The rubbed insulators able to retain charges placed on them so they were called dielectrics and rub conductors could not retain charges placed on them but immediately drained away the charges so they were called non electric I want to know the reason for this please explain me

An electron has kinectic energy 2.8*10^-23 j find de Broglie wavelength is

The mass of an oxygen molecule is about 16 times that of a hydrogen molecule. At room Temperature the rms speed of oxygen molecules is $v$. The rms speed of the hydrogen molecules at the same temperature will be

A heavy uniform rod is hanging vertically from a fixed support. It is stretched by its own weight. The diameter of the rod is

A stone is dropped from the top of a cliff and is found to travel 44.1m in the last second before it reaches the ground. Find the height of the cliff. (Can we use 1:3:5 method if yes then how)

Two particles A and B are thrown vertically upward with velocity, 5 m/s and 10 m/s respectively ($g=10m/s^2$). Find separation between them after one second. (Use relative motion approach)

A ball at rest is projected horizontally from a table in front of a vertical plane mirror as shown in the figure. At any time $t$, the velocity of image with respect to ground can be written as :

A current of $(2.5\pm 0.05)$ A flows through a wire and develops a potential difference of $(10\pm 0.1)$ volt. Resistance of the wire in ohm, is

In a series grouping of N cells, current in the external circuit is I. Number of cells to be reversed in polarity such that current becomes $\frac{I}{3}$ is

The container $A$ contains ice at $0^{\circ }\text{C}$. A conducting uniform rod $PQ$ of length $4R$ is used to transfer heat to the ice in the container. The end $P$ of the rod is maintained at ${100}^{\circ }\text{C}$ and the other end $Q$ is kept inside the container $A$. The complete ice melts in $23\text{minutes}$. In another experiments, two conductors in the shape of quarter circles of radii $2R$ and $R$ are welded to the conductor $PQ$ at $M$ and $N$ respectively and their other ends are inserted inside the container $A$. All conductors are made of the same material and have the same cross sectional area. Once again, the end $P$ is maintained at ${100}^{\circ }\text{C}$ and this time, the complete ice melts in $t\text{minutes}$. Find $t$.
[Assume no heat loss from the curved surface of the rods and take $\pi \simeq 3.0$]

A long straight neutral conductor carries a current l. Assume that all the free electrons in the conductor move with the same velocity v. A is a stationary observer while B is moving same velocity v parallel to the conductor

A hollow, neutral conducting sphere of inner radius $R_1$ and outer radius $R_2$ encloses a charge q inside it which is located at a distance d $(<R_1)$ from the centre of the spheres. The potential at the centre of the shell is

A uniform rod of mass $6kg$ is lying on a smooth horizontal surface. Its two ends are pulled by strings as shown in figure. Force exerted by $40cm$ part of the rod on $10cm$ part of the rod is

The mass per unit length of a rod of length $3$ $m$ is directly proportional to distance $x$ from its one end. The centre of mass of the rod from that end will be at

Two blocks of mass 4 kg and 2 kg are connected by a heavy string and placed on rough horizontal plane. The 2 kg block is pulled with a constant force F. The coefficient of friction between the blocks and the ground is 0.5. What is the value of F so that tension in the string is constant throughout during the motion of the blocks : $(g=10m/s^2)$

A rod of mass $m$ and length $2l$ hangs by two identical light threads tied to its ends. An insect of mass $\frac{3m}{8}$ lands on the rod gently at a distance $\frac{l}{3}$ from the centre of the rod as shown and sticks to it. As a result one of the thread breaks. The acceleration of the insect just after the thread breaks given that the insect remains at rest with respect to the rod.

A beam of cathode rays after gaining kinetic energy once it passes throught a potential difference of $V$ is subjected to crossed electric ($E$) and magnetic fields ($B$). The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by

In the figure shown capacitors A and B of capacitance C each are in steady state. A dielectric slab of dielectric constant K = 2 and dimensions equal to the inner dimensions of the capacitor is inserted in the space between the plates of the capacitor B. Choose the correct option(s):

A plane is in a level flight at a constant speed and each of its two wings has an area of $50{\text{m}}^2$. If the speed of air is $180\text{km/h}$ over the lower wing surface and $252\text{km/h}$ over the upper wing surface, the plane's mass is [Lift force on the wings = weight of plane]
(Take density of air = $1{\text{kg/m}}^3$ and $g=10{\text{m/s}}^2$)

What is the effect of the temperature on capacitance of a parallel plate capacitor.

1. 4

Ratio of the weights of a $1\text{kg}$ block of iron and $1\text{kg}$ block of wood as measured by a spring balance is:
Given: Density of iron $=7800{\text{kg/m}}^3$, density of wood $=800{\text{kg/m}}^3$ and density of air $=1.293{\text{kg/m}}^3$

If the force constant of the spring is $50\text{N/m}$. Find the mass of the block if it rests in the given situation. Take $g=10m/s^2$

A block is lying on a horizontal frictionless surface. One end of a uniform rope is fixed to the block which is pulled in the horizontal direction by applying a force $F$ at the other end. If the mass of the rope is half the mass of the block, the tension in the middle of the rope will be

A body is projected at ${30}^{\circ }$ with velocity $v_1$ from point $A$ on the ground. At the same time another body is projected vertically upwards from $B$ with velocity $v_2$ from the ground. The point $B$ lies vertically below the highest point of the trajectory of ball $A$. For both the bodies to collide, what should be the ratio of $v_1/v_2$ ?

Distance between successive compression and rarefaction is $1\text{m}$ and velocity of sound is $360{\text{ms}}^{-1}.$ Find the frequency of sound wave.

If the speed of the particle is $v=8t^3-3t^2+2\text{m/s}$, the distance of the particle as a function of time $t$ is

Assume that the temperature remains essentially constant in the upper part of the atmosphere. Obtain an expression for the variation in pressure with height in the upper atmosphere. The mean molecular weight of air is M. Assume a variable $P_O$ for the pressure at a height h = 0, where h = 0 depends on the choice of origin (could very well be at the beginning of the stratosphere, for example).

Which one of the following is the correct difference between Rod Cells and Cone Cells of our retina?

Classify the following as scalar and vector quantities:
(i) Time period
(ii) Distance
(iii) Force
(iv) Velocity
(v) Work done

Four point masses, each of mass $m$ are present at the four corners of a square of side length equal to $a$. Axis of rotation is passing through through one particle as shown in the figure below. The moment of inertia about the axis of rotation is

Is Lyman series continuous or not.?