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If a body takes 6 minutes to cool from 80⁰C to 70⁰C, how long will it take to cool from 60⁰C to 50⁰C, if the surrounding temperature is 25⁰C?

A wave is travelling along positive $x-$ direction with speed $4\text{m/s}$. Further, equation of the wave pulse at $t=0$ is $y(x,0)=\frac{5}{4+(3x+6{)}^2}$. The equation of the same pulse after $t\text{s}$ will be

A circular wire frame is made of two uniform semicircular wires of same radius and of mass per unit lengths $\lambda$ and $2\lambda$ as shown in figure. Which of the following options is/are true?

A T.V. tower has a height of 150 m. The area of the region covered by T.V. broadcast is (radius of earth = $6.4\times {10}^{6}m$)

A metal ball of mass $1.0\text{kg}$ is kept in a room at ${15}^{\circ }\text{C}$. It is heated using a heater. The heater supplies heat to the ball at a constant rate of $24\text{W}$. The temperature of the ball rises as shown in the graph. Assuming that Newton's law of cooling can be used, calculate the rate of heat loss from the ball when it is at a temperature of ${20}^{\circ }\text{C}$.

Two cubical blocks of side length $a$ and $2a$ are stuck symmetrically as shown in the figure. The combined block is floating in water with the bigger block just submerged completely. The block is pushed down a little and released. Find the time period of its oscillations. Neglect viscosity.

A wheel of $50\text{cm}$ radius rotates through ${360}^{\circ }$ around its axis. What is the distance travelled by a point on the edge of the wheel?

Water flows at a speed of $6cm{s}^{-1}$ through a tube of radius 1 cm. Coefficient of viscosity of water at room temperature is 0.01 poise. Calculate the Reynolds number. Is it a steady flow?

A uniform charged spherical shell has a total charge 2 C and radius 10 cm. With reference to infinity, self potential energy of the shell is .

A force $\overrightarrow{F}=3\hat{i}+2\hat{j}+c\hat{k}$ acts on a particle and causes a displacement $\overrightarrow{r}=c\hat{i}+4\hat{j}+c\hat{k}$ meter.

The work done is 36 joule.Find the value of 'c' ?

A simple pendulum has a time period $T$ in vacuum. Its time period when it is completely immersed in a liquid of density one-eighth of the density of the material of the bob is

A particle of mass $50\text{gm}$ is tied to a string of length $30\text{cm}$ is performing circular motion in a vertical plane. What will be the angular speed of particle, if tension in the string becomes zero at the top most position of circular path. (Take $g=10{\text{m/s}}^2$).

An object is thrown vertically upward with a velocity of $10m{s}^{-1}$ from the ground. It strikes the ground after____ seconds. (Take $g=10m{s}^{-2})$

Two buildings $A$ and $B$ are $20\text{m}$ apart. Building $A$ has a window at a height of $50\text{m}$ above the ground, and building $B$ has a window at height $30\text{m}$ from the ground. At what speed must a man throw a ball horizontally from the window of building $A$ so that it enters the window of building $B$. Take $g=10{\text{m/s}}^2$.

A block of mass $m=3\text{kg}$ is pulled by a force $F=50\text{N}$ upwards through $2\text{m}$ height in vertical direction. It takes $8\text{seconds}$ to lift the mass. Find the average power delivered by the force.

A 100 kg block is started with a speed of $2.0m{s}^{-1}$ on a long, rough belt kept fixed in a horizontal position. The coefficient of kinetic friction between the block and the belt is 0.20. 3. Consider the situation from a frame of reference moving at $2.0m{s}^{-1}$ along the initial velocity of the block. As seen from this frame, the block is gently put on a moving belt and in due time the block starts moving with the belt at $2.0m{s}^{-1}$

Calculate the increase in the kinetic energy of the block as it stops slipping past the belt.Find the work done in this frame by the external force holding the belt.

Potential energy of a particle along $x-$ axis is given by $U=[-20+(x-2{)}^2]\text{J}$. Force on the particle at $x=0$ is

The three rods of same material and crosssectional area form the sides of a triangle ABC. The points A, B and C are maintained at temperatures T, T$\sqrt{2}and\frac{3T}{(\sqrt{2}+1)}$ respectively. Assuming that only heat conduction takes place and the system is in steady state, find the angle at B. The temperature difference per unit length along CB and CA is equal.

Find the ratio of radii of gyration of a circular disc and a circular ring of same mass and radius, about an axis passing through their centre and perpendicular to their planes.

A mechanical wave propagates in a medium along the X-axis. The particles of the medium

Case 1: A balloon is fitted at the bottom of a cylinder which is half filled with water.
Case 2: A balloon is fitted at the bottom of a cylinder which is fully filled with water.
In which case will the balloon bulge more?

A hydrogen atom moving at a speed v absorbs a photon of wavelength 122 nm and stops. Find the value of v. Mass of a hydrogen atom $=1.67\times {10}^{-27}$ kg.

A large number of random snapshots using a camera are taken of a particle in simple harmonic motion between x = -
$x_0$ ​ and x = +
$x_0$ ​ with origin x = 0 as the mean position. A histogram of the total number of times the particle is recorded about a given position (Event no.) would most closely resemble

In the pulleys system as shown in the figure a particle of mass m falls from a height $h_0$ on the mass m and gets stuck to it. Speed with which the system moves just after the collision is:

Two capacitor $C_1$ and $C_2$ of capacity $6\mu F$ and $3\mu F$ respectively are charged to 100V and 50V separately and connected as shown in the figure. Now all the switches $S_1,S_2$ and $S_3$ are closed.

Suppose $q_1,q_2$ and $q_3$ be the magnitude of charges flown from switches $S_1,S_2$ and $S_3$ after they are closed. Then,

A parallel beam of light of intensity $I$ and cross section area $S$ is incident on a plate at normal incidence. The photoelectric emission efficiency is $100\%$, the frequency of beam is $v$ and the work function of the plate is $\varphi (hv>\varphi )$. Assuming all the electrons are ejected normal to the plane and with same maximum possible speed. The net force exerted on the plate only due to striking of photons and subsequent emission of electron is

A body traveling along a straight line traversed first one third of the total distance with a velocity $4\text{m/s}$. The remaining part of the distance was covered with a velocity $2\text{m/s}$ for half the time and with velocity $6\text{m/s}$ for the other half of time. The mean velocity over the whole time of motion is

A flat coil of $500$ turns, each of area $50c{m}^2$, rotates in a uniform magnetic field of $0.1Wb/m^2$ about an axis normal to the field at an angular speed of $150rad/s$. (Initially magnetic field was along the area vector of the field). The coil has a resistance of $15\Omega$. Maximum induced current in the coil is

Here three blocks A, B and C are connected with strings and pulleys as shown in figure. The constraint relation between the acceleration of masses A, B, and C can be formulated as?

A body falling freely from a given height $H$, hits an inclined plane in its path at a height $h$. As a result of this impact the direction of velocity of the body becomes horizontal. For what value of $\frac{h}{H}$ will the body take maximum time to reach the ground?

A cube has sides of length L = 0.300 𝑚. It is placed with one corner at the origin as shown in the
figure. The electric field is not uniform, but it is given by $\overrightarrow{E}=(-5.00N{C}^{-1})x\hat{i}+\left(3.00N{C}^{-1}\right)z\hat{k}$.
The total electric charge inside the cube is

The Bat Life: In the same example, if somehow, instead of changing the mass on the piston in a single step by a finite value, the mass on the piston was reduced by infinite steps by removing an extremely small mass in each step, which amongst these graphs represent(s) the new process? Remember that through each infinitesimally small change, the temperature remains constant.

In the following graph, distance travelled by the body in metres is

An L-C-R circuit is equivalent to a damped pendulum. In an L-C-R circuit, the capacitor is charged to $Q_0$ and then connected to $L$ and $R$ as shown. If a student plots graphs of the square of maximum charge $\left(Q_{Max}^2\right)$ on capacitor with time ($t$) for two different values $L_{1}and{L}_2(L_1>L_2)$ of $L$, then which of the following represents this graph correctly? (Plots are schematic and not drawn to scale)

If $y=1/x^4,$ then $\frac{dy}{dx}$ will be

A gun of mass 5kg fire a bullet of mass 5g vertically upward to a height of 100m. Calculate the recoil velocity of the gun.

A man in a balloon throws a stone downwards with a speed of 5 m/s with respect to balloon. The balloon is moving upwards with a constant acceleration of $5m/s^2$Then velocity of the stone relative to the man after 2 second is

A gas mixture of $2$ moles of $O_2$ and $4$ moles of $Ar$ are at temperature $T$. Neglecting all the vibrational modes, the total internal energy of the system is

Find the average velocity of a projectile between the instants it first crosses half the maximum height and then again does the same. It is projected with a speed $u$ at an angle $\theta$ with the horizontal. (no need to calculate, just work it out mentally!).

The velocity of water near the surface of river is 5 m/s whereas the depth is 5m. The coefficient of viscosity of water is ${10}^{-2}$ poise, then shearing stress will be

100kg of iron and cotton are weighed by using a spring balance on surface of earth. If R1 and R2 are the readings shown by balance thwn R1 >R2. Why?