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A particle moves with deceleration along the circle of radius $R$ so that at any moment of time its tangential and centripetal accelerations are equal in moduli. At the initial moment $t=0$, the speed of the particle equals $v_0$. Then



The speed of the particle as a function of the distance covered $s$ will be

The resistance of a wire is $10\Omega$. It's length is increased by $10\%$ by stretching. The new resistance will now be

A man wishes to cross a river in a boat. If he crosses the river in minimum time he takes 10 minutes with a drift of 120 m. If he crosses the river taking shortest route, he takes 12.5 minutes, find velocity of the boat with respect to water.

What is continuous charge distribution?

The excess pressure inside one soap bubble is three times that inside a second soap bubble, then the ratio of their surface areas is:

A particle moves in a circular path of radius $20\text{cm}$ as shown. Find angular velocity of particle w.r.t an axis passing through centre of the circle and perpendicular to plane of the circle.

A uniform solid cube is floating in a liquid as shown in the figure, with length $x$ inside the liquid. Some changes in parameters are mentioned in Column I. Assuming no other changes, match the following.



$\begin{array}{cc}\text{(A) If density of the liquid decreases,}x\text{will}& \text{(P) Increase}\\ \text{(B) If height of the cube is increased keeping base area and density same,}x\text{will}& \text{(Q) Decrease}\\ \text{(C) If the whole system is accelerated upward, then}x\text{will}& \text{(R) Remain same}\\ \text{(D) If the cube is replaced by another cube of same size but lesser density,}x\text{will}& \text{(S) either increase or decrease}\end{array}$



Which of the following option has the correct combination considering column-I and column-II.

Three liquids of densities $d,2d$ and $3d$ are mixed in equal proportions of weights. The relative density of the mixture is

A particle executes SHM of period $\pi$ and amplitude 2cm. Find the acceleration of particle when it is 1 cm from mean position.

A super conductor has $T_c\left(0\right)=100K.$ When a magnetic field of $7.5$ Tesla is applied , its $T_c$ decreases to $75K$. For this material one can definitely say that when

A system of a circular disc of mass $900\text{g}$ and radius $4\text{m}$ and a circular ring of mass $2\text{kg}$ and radius $5\text{m}$ are stacked about their common centre as shown in figure. What is the moment of inertia of the system about an axis passing through their common centre perpendicular to the plane of the disc and the ring?

The resultant of two velocity vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is perpendicular to $\overrightarrow{A}$. The angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is ${150}^{\circ }$. Find $\frac{|\overrightarrow{R}|}{|\overrightarrow{B}|}$ where $\overrightarrow{R}$ is the resultant vector.

A ball of mass $m$ falls from rest under gravity in a resisting medium (Exerting drag during motion). The resistance force is given by $f=kv$, which can be considered as a friction force offered by the resisting medium. The correct velocity $\left(v\right)$ versus time $\left(t\right)$ graph for body is:

Calculate the frequency of beats produced in air when two sources of sound are activated, one emitting a wavelength of 32 cm and the other of 32.2 cm. The speed of sound in air is 350 m/s.

Resistance of a resistor at temperature $t^{\circ }C$ is $R_t=R_0(1+at+b{t}^2)$; where $R_0$ is the resistance at $0^{\circ }C.$ The temperature coefficient of resistance at temperature $t^{\circ }C$ is

The velocity of photon is proportional to (where v is frequency)

A metallic rod of length $l$ is tied to a string of length $2l$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $B$ in the region, the e.m.f. induced across the ends of the rod is:

Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by $75\times {10}^{-4}\text{N}$ force due to the weight of the liquid. If the surface tension of water is $6\times {10}^{-2}\text{N/m}$, the inner circumference of the capillary tube must be: (Take $\theta =0^{\circ })$

A particle starts from the origin at time $t=0$ and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time $t=5\text{s}$ ?

If potential energy density is twice the average rate of transmission of potential energy. The speed of transverse wave is

What is an adsorption
isotherm? Describe Freundlich adsorption isotherm.

An object $\text{A}$ is kept fixed at the point $x=3\text{m}$ and $y=1.25\text{m}$ on a plank $\text{P}$. At time $t=0$, the plank starts moving along the $+x$ - direction with an acceleration $1.5{\text{m/s}}^2$. At the same instant, a stone is project from the origin with a velocity $\overrightarrow{u}$ as shown. A stationary person on the ground observes the stone hitting the object during its downward motion at an angle of ${45}^{\circ }$ to the horizontal. All the motions are in $x-y$ plane. The velocity $\overrightarrow{u}$ is

The following can be arranged in decreasing order of wave number as

$A$. Radio wave

$B$. Microwave

$C$. X-Ray

$D$. Visible Ray

1. 7.71

A small ball of mass $m$ is connected by an inextensible massless string of length $l$ with another ball of mass $M=4m$. They are released with zero tension in the string from a height $h$ as shown in the figure. The time $t$ after which the string becomes taut for the first time after the mass $m$ collides with the ground is (Assume all the collisions to be elastic)

A dam is situated at a height of 550 metres above sea level and supplies water to a power house which is at a height of 50 metres above sea level. 2000 kg of water passes through the turbines per second. The maximum electrical power output of the power house if the whole system were $80\%$ efficient is

Two blocks are moving as shown. The ratio of$\frac{v_1}{v_2}$ is

Two ends of a conducting rod of varying cross-section are maintained at ${200}^{\circ }\text{C}$ and $0^{\circ }\text{C}$ respectively. In staedy state