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A car is moving with speed 30 m/sec on a circular path of radius 500 m.
Its speed is increasing at the rate of 2m/$se{c}^2$, What is the acceleration of the car

A man of mass $80\text{kg}$ jumps from a trolley of mass $20\text{kg}$ standing on a smooth surface, with an absolute velocity of $3\text{m/s}$. The recoiling speed of the trolley is

A projectile of mass $0.5kg$ is thrown with a velocity of $30m/s$ at an angle of ${60}^{\circ }$ with the horizontal. Find the net force acting on the body.

A body moves a distance of 10 m along a straight line under the action of a force of 5 N. If the work done is 25 joule, the angle which the force makes with the direction of motion of the body is

In the figure shown, find the acceleration (in $m/s^2$) of the blocks if the wedge is fixed. (String is massless and inextensible)

Four capacitors of capacitance $C_1=1\mu \text{F},C_2=2\mu \text{F},C_3=3\mu \text{F}$ and $C_4=4\mu \text{F}$ are connected as shown in the figure. Find the potential differences across $C_3$ when switch $S$ is closed.

Find the area enclosed by the curve $y=x^2$ and the x-axis for interval x = 1 to x = 3.

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The maximum speed with which a vehicle can negotiate a curved road, which is banked at the angle, $\theta ={\tan }^{-1}\left(0.24\right)$ is $54\text{km/hr}$. If another road is flat and the vehicle has to negotiate a curve with the same maximum speed, coefficient of friction between road and tyre should be

(Radius of both the road is same)

If $I_1,I_2\text{and}{I}_3$ are the intensities of three radiations incident on the same metal surface with the same frequency such that $(I_1>I_3>I_2)$ and following graph of variation of photo current with respect to anode potential is observed. Find which curve represents the three intensities.

Two identical wires $\text{A}$ and $\text{B}$ each of length $L$, carry the same current $I$. Wire $\text{A}$ is bent into a circle of radius $R$ and wire $\text{B}$, is bent to form a square of side $a$. If $B_{\text{A}}$ and $B_{\text{B}}$ are the values of magnetic fields at the center of circle and square then the ratio of $\frac{B_{\text{A}}}{B_{\text{B}}}$ is

The double slit experiment of Young has been shown in figure. Q is the position of the first bright fringe on the right side and P is the ${11}^{th}$ bright fringe on the other side as measured from Q. If wavelength of the light used is $6000A^{\circ },$ then $S_{1}B$, will be equal to

The displacement (in $\text{m}$) equation of a particle is $x=3\text{sin}2t+4\text{cos}2t$. The amplitude (in $\text{m}$) and maximum velocity (in $\text{m/s}$) will be respectively.

In the shown figure, answer the following question.



If $p_i,p_r,p_t$ are powers of incident, reflected and transmitted waves and $I_i,I_r,I_t$ the corresponding intensities, then under what conditions $75\%$ of incident energy is transmitted?

Electromagnetic radiation with an energy flux of $10{\text{W cm}}^{-2}$ falls on a reflecting surface at normal incidence. The surface has an area of $20{\text{cm}}^2$, what is average force exerted on surface during a $30$ minute time span ?

The resistance of carbon filament at $0^{\circ }$C is $104\Omega$. It is connected in series to an iron wire. The temperature coefficient of resistance of carbon and iron are $-0.0003/{}^{\circ }$C and $+0.0052/{}^{\circ }$C respectively. What must be the resistance of iron wire so that the combined resistance does not change with temperature?

Three blocks of masses $m_1$, $m_2$ and $m_3$ are connected by massless strings as shown in the figure and placed on a frictionless table. They are pulled with a force $T_3=40N$. The tension $T_2$ will be: (Given $m_1=10kg,m_2=6kg$ and $m_3=4kg$)

Two identical short magnetic dipoles of magnetic moments $1.0{\text{Am}}^2$ each, placed at a separation of $2\text{m}$ , with their axes perpendicular to each other. The resultant magnetic field at a point midway between the dipole is-

Two wires of equal length and cross-section are suspended as shown. Their Young’s modulii are $y_1$ and $y_2$ respectively. The equivalent Young’s modulus will be

Figure represents a capacitor made of two circular plates each of radius $r=12\text{cm}$ and separated by $d=5.0\text{mm}$. The capacitor is being charged by an external source. The charging current is constant current, $I=0.15\text{A}$.

Calculate the rate of change of electric field between the plates.

Two equal and positive charges are placed at $a$ and $-a$ on $x$-axis, then graph of electric field along $x$-axis with distance $x$ will be

A wire of length 2.00 m fixed at both the ends is stretched to a tension of 160 N. if the fundamental frequency of vibration is 100 Hz, find its linear mass density.

Find the equivalent inductance between $\text{A}$ and $\text{B}$ is-

A uniform heavy chain of length 'a' initially has length 'b' hanging off of a table. The remaining part of chain a - b, is coiled on the table. If the chain is released, the velocity of the chain when the last link leaves the table is