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As the object moves towards a concave mirror from infinity, the image will

A $50\text{kg}$ girl is swinging on a swing. Then, the power delivered while moving with a velocity of $2\text{m/s}$ upwards and the rope makes an angle of ${60}^{\circ }$ with the vertical is



$($Assume girl starts from rest and $g=9.8{\text{m/s}}^2)$

A force $F=a+bx$ acts on a particle in the $x$ - direction, where $a$ and $b$ are constants. Find the work done by this force during a displacement from $x=0$ to $x=d$.

The upper half of an inclined plane with inclination $\theta$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom, then the coefficient of kinetic friction for the lower half is given by

Find the tension (in $N$) acting on $2m$ mass when the system is released from rest. Assume that the pulleys are ideal and strings are inextensible.

The average energy and the rms speed of molecules in a sample of oxygen gas at $300\text{K}$ are $6.21\times {10}^{-21}\text{J}$ and $484{\text{ms}}^{-1}$ respectively. The corresponding values at $600\text{K}$ are nearly

A body initially moving with a velocity of $5{\text{ms}}^{–1}$, attains a velocity of $25{\text{ms}}^{–1}$ in $5s$. The acceleration of the body is:

(Assume constant acceleration)

The diameter of a brass rod is 4 mm and Young’s modulus of brass is $9\times {10}^{10}\frac{N}{m^2}$. The force required to stretch by 0.1% of its length is

If $y=x^3+2x^2+7x+8$, then $\frac{dy}{dx}$ will be

Two wires of the same material (Young’s modulus Y) and same length L but radii R and 2R respectively are joined end to end and a weight w is suspended from the combination as shown in the figure. The elastic potential energy in the system is :

If angular position of a particle $\theta$ depends on time $t$ as $\theta =2t^2+3$, find the average angular velocity at the end of $3\text{sec}$ and instantaneous angular velocity at $t=3\text{sec}$ (in $rad/s$)

The equation of motion of a particle started at $t=0$ is given by $x=10\text{sin}(20t+\frac{\pi }{3})$, where $x$ is in $\text{cm}$ and $t$ is in seconds. Find the time when the particle first comes to rest.

A body is projected vertically upwards with a speed of $\sqrt{\frac{GM}{R}}$. The body will attain a height of

$(M$ is mass and $R$ is Radius of earth$)$

If mass of the electron $=9.1\times {10}^{-31}\text{kg}$, charge on the electron $=1.6\times {10}^{-19}\text{C}$ and $g=9.8{\text{ms}}^{-2}$. Then, the intensity of the electric field required to balance the weight of an electron is -

1. 1

Two vectors, both equal in magnitude, have their resultant equal in magnitude to any of the two vectors. Find the angle between the vectors.

Find the following integrals.
$\int \frac{2-3sinx}{co{s}^{2}x}dx.$

If a spring of spring constant $k$ is divided into $m$ equal parts, and all are connected in parallel, then the equivalent spring constant of the combination is

Figure 3.25 gives a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest? Choosing the positive direction as the constant direction of motion, give the signs of v and a in the three intervals. What are the accelerations at the points A, B, C and D?

(Fig: 3.25)

In two experiments with a continuous flow calorimeter to determine the specific heat capacity of a liquid, an input power of 60 W produced a rise of 10 K in the liquid. When the power was doubled, the same temperature rise was achieved by making the rate of flow of liquid three times faster. The power lost to the surrounding in each case was :

A copper wire bent in the shape of a semicircle of radius r translates in its plane with a constant velocity v. A uniform magnetic field B exists in the direction perpendicular to the ends of the wire if

(a) The velocity is perpendicular to the diameter joining free ends,

(b) The velocity is parallel to this diamneter.

In figure the angle of inclination of the inclined plane is ${30}^{\circ }$. Find the horizontal velocity $V_0$ so that the particle hits the inclined plane perpendicularly.

Two narrow bores of diameter $5.0\text{mm}$ and $8.0\text{mm}$ are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube.



$\text{Take surface tension of water,}T=7.3\times {10}^{-2}{\text{Nm}}^{-1}$

$\text{angle of contact}=0$

$g=10{\text{ms}}^{-2}$

$\text{density of water}=1.0\times {10}^3{\text{kgm}}^{-3}$

In a region, steady and uniform electric field and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a:

An angry bird (flightless) of mass 5 kg is projected with a speed of 25 m/s at an angle of ${37}^{\circ }$ with the horizontal. When it reaches its maximum height, it screams "fire in the hole!” and decides to take a massive 1 kg dump on Ram standing directly below it. What will be the magnitude of the horizontal velocity of the bird after release?

A body is projected at such an angle that the horizontal range is three times the greatest height. The angle of projection is

In SI unit number of electric field line associated with 1 coulomb charge is

The linear density of a vibrating string is ${10}^{-4}kg/m$. A transverse wave is propagating on the string, which is described by the equation y = 0.02 sin (x + 30 t), where x and y are in meters and time t in seconds. Then tension in the string is