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A painter of mass $100\text{kg}$ is raising himself and the crate (such an arrangement is called Bosun's chair) on which he stands as shown. When he pulls the rope the force exerted by him on the crate's floor is $450\text{N}$. If the crate weighs $25\text{kg}$ then, find the acceleration of the system and the tension in the rope.

At t = 0, a transverse wave pulse travelling in the positive x direction with a speed of 2 m/s in a wire is described by the function $y=\frac{6}{x^2}giventhatx\ne 0$. Transverse velocity of a particle at x = 2 m and t = 2 s is

A bimetallic strip on heating has radius $R$. The coefficients of thermal expansion are ${\alpha }_1$ and ${\alpha }_2$. If the strip having greater coefficient of thermal expansion $\left({\alpha }_1\right)$ is replaced by an identical strip having coefficient of thermal expansion $3$ times its value (i.e $3{\alpha }_1$) and heated to the same temperature difference, then the new radius of the arc is

[ given, $\frac{{\alpha }_1}{{\alpha }_2}=2$ ]

A disc of radius $2cm$ rotating uniformly about a stationary axis with an angular velocity of $10rad/s$ is now experiencing an angular retardation of $\alpha =0.2t$. The magnitude of centripetal acceleration at $t=2s$ is

Each of the pictures shows four objects tied together with rubber bands being pulled to the right across a horizontal frictionless surface by a force $F$. All the objects have the same mass. All the rubber bands obey Hooke’s law and have the same equilibrium length and the same force constant. Which of the pictures is drawn most correctly?

A horizontal disc rotating freely about a vertical axis through its centre makes $90$ revolutions per minute. A small piece of wax of mass $m$ falls vertically on the disc and sticks to it at a distance $r$ from the axis. If the number of revolutions per minute reduces to $60$, the moment of inertia of the disc is

An aeroplane is flying horizontally with a velocity of 600 km/h at a height of 1960 m. When it is vertically above a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is

A spring 40 mm long is stretched by the application of a force. If 10 N force required to stretch the spring through 1 mm, then work done in stretching the spring through 40 mm is

A particle of mass M at rest decays into two particles of masses $m_1$ and $m_2$, having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles, $\frac{{\lambda }_1}{{\lambda }_2}$ is

A brass cube of side $a$ and density $\sigma$ is floating in mercury of density $\rho$. If the cube is slightly displaced vertically, it executes $SHM$. Its time period will be

The unit of surface tension in the $\text{CGS}$ system is

Find the accelerations $a_1,a_2$ and $a_3$ of the three blocks as shown in figure, if a horizontal force of $10\text{N}$ is applied on the $3\text{kg}$ block. The coefficient of static friction ($\mu$) for all contact surfaces are shown in the figure. Take $g=10{\text{m/s}}^2$.

In Coolidge tube electrons were ejected by the cathode because of which method:

Velocity of the boat with respect to river ($v_{b/r}$) is $10m/s$. It passes the river of width $36m$ and reaches opposite shore at point $R$ shown in the figure. If the velocity of the river is $3m/s$, find the time of the trip and drift of the boat.

A point charge 'q' is placed at a distance 'l' from the centre of a disc of radius 'R' along its axis. The electric flux through the disc is

A standing wave is produced in a $10\text{m}$ long string fixed at one end and free at the other end. Find the wavelength of wave, if string is vibrating in its second overtone, and wave velocity is $20\text{m/s}$.

Five gas molecules chosen at random are found to have speed of $500\text{m/s},600\text{m/s},700\text{m/s},800\text{m/s}$ and $900\text{m/s}$. The approximate rms speed is :

If $F_1=10\text{N}$ and $F_2=15\text{N}$ as shown in the figure, the resultant $R$ will be [Hint: $\cos {65}^{\circ }=0.423$]

A box and a capacitor C are in series across an AC source of $w=2rad{s}^{-1}$. The power factor of the box is $\frac{1}{\sqrt{2}}$ and that of the circuit is 1. Find the impedance of the box.

A proton, a deuteron and an $\alpha -$ particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If $r_p,r_d$ and $r_{\alpha }$ denote the radii of the trajectories of these particles respectively, then

A block of mass $4\text{kg}$ is kept on an inclined plane having an angle of inclination ${37}^{\circ }$ attached with a spring of force constant $20\text{N/m}$ as shown in the figure. If the coefficient of friction between the block and incline is $0.8$, find the range in which the block can be at rest without slipping from its equilibrium position?

In Galileo's experiment in order to reach the same height how far must the ball go on the horizontal surface after being released from an incline of a height of 5m?

Between the two stations, a train uniformly accelerates from rest at first, then moves with constant velocity and finally decelerates uniformly to come to rest. If the ratio of the time taken is $1:8:1$ and the maximum speed attained is $60\text{km/h}$, then what is the average speed over the whole journey?

Nature of meniscus for liquid of $0^{\circ }$ angle of contact

Two bodies are projected with the same velocity. If one is projected at an angle of ${30}^{\circ }$ and the other at an angle of ${60}^{\circ }$ to the horizontal, the ratio of the maximum heights reached is

The maximum stress that can be applied to the material of a wire used to suspend an elevator is ${10}^8{\text{Nm}}^{-2}$. If the mass of the elevator is $1000\text{kg}$ and it moves up with an acceleration of $0.2{\text{ms}}^{-2}$, what is the minimum diameter of the wire required? (Take $g=9.8\text{m}/{\text{s}}^2$)

A body undergoes a free fall. Taking downward direction as +ve $Y$ direction and $Y_o$ is the initial position, $Y$ coordinate at any time $t$ is given by

Potential energy of a satellite having mass ‘m’ and rotating at a height of $6.4\times {10}^6$ from the earth centre is

A block is placed on a rough horizontal plane. A time dependent horizontal force F = Kt acts on the block. Here, K is positive constant. Acceleration - time graph of the block is

In order to find out the amount you must change the time on your clock, which of this is sufficient?

Figure shows three containers. The rightmost container contains water (heat capacity $5cal{/}^{\circ }C$), initially at temperature ${100}^{\circ }\text{C}$. The middle container contains water maintained at ${80}^{\circ }\text{C}$ with the help of a heater. The container at the left hand side contains ice at $0^{\circ }\text{C}$. There are two heat conducting rods $A$ and $B$ both having thermal resistance equal to ${10}^{\circ }\text{C}\text{s/cal}$. Disregard any heat loss in the surrounding.





Initially, what is the power of heater required to maintain the temperature of middle container at ${80}^{\circ }\text{C}$?

In the figure shown below, two rods are maintained at the same temperature difference between the ends. As a result, heat is flowing through two rods made of the same material. If the diameters of the rods are in the ratio $1:4$ and their lengths are in the ratio $3:2$, then find the ratio of the rates of flow of heat through them.

Galileo writes that for angles of projection of a projectile at angles (45 + $\theta$) and (45 - $\theta$), the horizontal ranges described by the projectile are in the ratio of (if $\theta$ < 45)

At time t = 5 secs, Can you predict which floor the elevator will be on if nobody stops the elevator and there are enough floors in the building.

A toy cart is tied to the end of an unstretched string of length $‘l^{\prime }$, when revolved, the toy cart moves in horizontal circle with radius $‘2l^{\prime }$ and time period $T_1$. If it is speeded until it moves in horizontal circle of radius $‘3l^{\prime }$ with period $T_2$, relation between $T_1$ and $T_2$ is (Hooke’s law is obeyed)

Consider the figure. Each capacitor has capacitance C.



The capacitance between 1 and 3 is

In an atom, the two electrons move round the nucleus in circular orbits of radii R and 4R. The ratio of the time taken by them to complete one revolution is

A rectangular loop of sides $10\text{cm}$ and $5\text{cm}$ with a cut, is stationary between the pole pieces of an electromagnet. The magnetic field of the magnet is normal to the loop. The current feeding the electromagnet is reduced so that the field decreases from its initial value of $0.3T$ at the rate of $0.02T{s}^{-1}$. If the cut is joined and the loop has a resistance of $2.0\Omega$, the power dissipated by the loop as heat is

A body of mass $3\text{kg}$ is under a constant force has displacement $s$, given by the relation $s=\frac{1}{3}{t}^2$, where $t$ is in seconds, $s$ is in metres. Work done by the force in $2$ seconds is

The gravitational potential in a region is given by V = (3x + 4y + 12z)$\frac{J}{kg}$. The modulus of the gravitational field at (x = 1, y = 0, z = 3) is

If you are pushing the wall then the wall will also push you back according to 3rd law.. so which is action and which is reaction.

The equation for the vibration of a string, fixed at both ends vibrating in its third harmonic, is given

$y=\left(0.4cm\right)sin\left[\right(0.314c{m}^{-1}\left)x\right]cos\left[\right(600\pi s^{-1}\left)t\right]$

i. What is the frequency of vibration?

ii. What are the positions of the nodes?

iii. What is the length of the string?

iv. What is the wavelength and the speed of two travelling waves that can interfere to give this vibration?

Find the variation of ${ϵ}_{ind}$ vs time for the following system.

The first overtone frequency of a closed organ pipe is equal to the second overtone frequency of an open organ pipe. If the length of the open pipe is $80\text{cm}$, what is the length of the closed organ pipe?

In a very long solenoid of radius $R$, if the magnetic field changes at the rate of $\frac{dB}{dt}$, the induced emf for the triangular circuit ABC as shown in the figure is (AB=BC)

For the system shown in the figure, assume that the cylinder remains in contact with the two wedges moving with constant velocity as indicated. What will be the velocity of cylinder?

A two dimensional lamina of arbitrary shape is placed in $x-y$ plane as shown in the figure. $\text{MOI}$ of lamina about $x$ and $y$ axes are $I_x=6{\text{kg-m}}^2$ and $I_y=4{\text{kg-m}}^2$ respectively. If point of intersection $\left(O\right)$ of the axes does not lies on lamina, then the $\text{MOI}$ of lamina about $z$ axis i.e. $\left(I_z\right)$ will be