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A player kicks a football at an angle of ${45}^{\circ }$ with a velocity of $20m{s}^{-1}$. A second player on the goal line $60m$ away in the direction of kick starts running to receive the ball at that instant. Find the speed $\left(m/s\right)$ of the second player with which he should run to strike the ball before it strikes the ground $(g=10m{s}^{-2})$

Indiborane

In the figure shown below, $m_A=2\text{kg}$ and $m_B=4\text{kg}$. For what minimum value of $F$, $A$ starts slipping over $B$. (Take $g=10{\text{m/s}}^2$)

A circular coil of radius $R$ carries an electric current $I$. The magnetic field due to the coil at a point on the axis of the coil located at a distance $r$ from the centre of the coil, such that $r>>R$, varies as

The electric field in a region of space is given by $\overrightarrow{E}=5\hat{i}+2\hat{j}{\text{NC}}^{-1}$. The electric flux due to this field through an area $2{\text{m}}^2$ lying in the $yz$- plane in S.I units is

In a bolted joint two smooth members are connected with an axial tightening force of $2200N$.If the bolt used has metric threads of $4mm$ pitch, the torque required for achieving the tightening force is

If I dropped a Metal ball of weight 10kg and a feather and If I can Imagine that there is no air resistance, then,. Which do you think will reach the ground first?

A monorail crane runs on an I - section of span 8 m which is simply supported. The crane capacity is 20 kN and crab weight is 4 kN. Use impact factor as 25% and $El=10\times {10}^{12}Nm{m}^2$. The deflection for the crane will be mm. [Deflection due to self weight is neglected]

1. 25.6

A conductor in the form of a right angle $ABC$ with $AB=3\text{cm}$ and $BC=4\text{cm}$ carries a current $10\text{A}$. There exists a uniform magnetic field of magnitude $5\text{T}$ perpendicular to the plane of conductor. The magnetic force acting on conductor will be: (Assume the conductor is in gravity free space)

Number of electric lines of force from 0.5 C of positive charge in a dielectric medium of dielectric constant 10 is

The angle between $\overrightarrow{A}$ and resultant of $(\overrightarrow{A}+\overrightarrow{B})$ and $-\overrightarrow{B}$ is

A metallic square loop ABCD is moving in its own plane with velocity v in a uniform magnetic field perpendicular to its plane as shown in Fig. 25.25. An electric field is induced

When a wave travels in a medium, the particle displacement is given by

$y(x,t)=0.03sin\pi (2t-0.01x)$

where y and x are expressed in metres and t in seconds. At a given instant of time, the phase difference between two particles 25 m apart is

A rod has actual length at ${20}^{\circ }\text{C}$. Find the highest possible temperature at which the length should be measured, so that the error in measurement do not exceed $0.01\%$. The thermal coefficient of linear expansion is $2\times {10}^{-5}{/}^{\circ }\text{C}$

Potentiometer wire length is $10\text{m}$, having a total resistance of $75\Omega$ and a battery of emf $200\text{V}$ (of negligible internal resistance) connected to it as shown in figure. Find the value of $x$ if $\text{P}$ is a null point.

If one joule of energy is converted to a new system of units in which length is measured in 10m, mass in 10 kilogram and time in 1 minute.What is the value of energy in this new system.

A laser beam of visible light is shined perpendicular to a magnetic field. Which of the following may happen

A satellite is launched into a circular orbit of radius $R$ around the earth. A second satellite is launched into an orbit of radius $1.01R$. The time period of the second satellite is larger than that of the first one by approximately

A block of ice at $–{10}^{\circ }C$ is slowly heated and converted to steam at ${100}^{\circ }C$. Which of the following curve represents the phenomenon qualitatively?

What
is the density of water at a depth where pressure is 80.0 atm, given
that its density at the surface is 1.03 × 10³
kg m^–3?

A stone falls freely under gravity. It covers distances h_1, h_2, h₃ in the first 5 seconds , the next 5 seconds and the next 5 seconds respectively. What is the relation between h_1, h₂ and h_{3 .}

The moment of inertia of a body about a given axis is $1.2\text{kg}-{\text{m}}^2$. Initially, the body is at rest. In order to produce a rotational kinetic energy of $1500\text{J}$, an angular acceleration of $25{\text{rad/s}}^2$ must be applied about that axis for a duration of

An ideal gas expands adiabatically against vacuum. Which of the following is correct for the given process?

All transistors in the N output mirror shown below are matched with a finite gain $\beta$ and early voltage $V_A=\infty$. The expression for each load current is

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

A pendulam has a time period $T$ for small oscillations. An obstacle $\text{P}$ is situated below the point of suspension $\text{O}$ at a distance $\frac{3l}{4}$ as shown in the figure below. The pendulum is released from rest. Throughout the motion the moving string makes small angle with vertical. Find the time after which the pendulum returns back to its initial position.

Two convex lenses, each of focal length 1.0 cm, are placed at a separation of 15 cm with their principal axes coinciding.

(a) Show that a light beam coming parallel to the principal axis diverges as it comes out of the lens system.

(b) Find the location of the virtual image formed by the lens system of an object placed far away.

A 350 kg boat is 12 m long and is floating without motion on still water. A boy of mass 50 kg is at one end. The boy walks to the other end of the boat and stops. The distance in meters moved by the boy with respect to the shore is

On a particular day, the maximum frequency reflected from the ionosphere is $10\text{MHz}$. On another day, it was found to increase to $11\text{MHz}$. Calculate the ratio of maximum electron density of the ionosphere on the two days.