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A body is weighed by a spring balance to be 1.000 kg at the north pole. How much will it weigh at the equator ? Account for the earth's rotation only.

A point moves along a circle with velocity $v=at,$ where $a=0.5{\text{m/s}}^2$. Then the total acceleration of the point at the moment, when it has covered ${\left(\frac{1}{10}\right)}^{th}$ of the circle after the beginning of motion is

If the forward voltage in a semiconductor diode is doubled, the width of the depletion layer will

Two radioactive samples of different elements having half lives $t_1$ and $t_2$ respectively, have the same number of nuclei at $t=0$. The time after which their activities are the same is

An electric bulb is rated as $100\text{V}$ and $50\text{W}$. When it is operated at $20\text{V}$, the power consumed will be -

Two balls $A$ and $B$ are thrown with speed $u$ and $\frac{u}{2}$ respectively. Both the balls cover the same horizontal distance before returning to the horizontal plane of projection. If the angle of projection of ball $B$ is ${15}^{\circ }$ with the horizontal, then the angle of projection of $A$ is

A wire increases by ${10}^{-3}$ times of its length when a stress of $1\times {10}^8{\text{Nm}}^{-2}$ is applied to it in the longitudinal direction. Ratio of longitudinal stress and longitudinal strain in the wire is

Three discs having same mass $M$ and radius $R$ are placed as shown in figure. Then the moment of inertia of system about axis $AB$ in the given arrangement is –

• If the length of the wrench used had been $0.3\text{m}$ instead, would it have been easier for him to open the nut?


• Prove your statement by finding the effort needed in case of using the shorter wrench.

A bullet of mass 0.01 kg and travelling at a speed of 500 ms^-1 strikes a block of mass 2 kg, which is suspended by a string of length 5 m. The center of gravity of the block is found to rise a vertical distance of 0.1 m. What is the speed of the bullet after it emerges from the block ?

In the Wheatstone bridge shown below the galvanometer G has a current sensitivity of $1\mu A/mm,$ a resistance of $2.5k\Omega$ and a scale resolution of 1 mm. Let $\Delta R$ be the minimum increase in R from its nominal value of $2k\Omega$ that can be detected by this bridge.



The value of $\Delta R$ is approximately

A wire of resistance $12\Omega /\text{m}$ is bent to form a complete circle of radius $10\text{cm}$. The resistance between its two diametrically opposite points, $A$ and $B$ as shown in the figure is -

The effective resistance between the points $P$ and $Q$ of the electrical circuit shown in the figure is

The gravitational field in a region is given by $E=(2\hat{i}+3\hat{j})N/kg$. The equation of the line on which no work is done by the gravitational when the particle is moved

The measurement of the position of the electron is associated with an uncertainty in momentum, which is equal to $1\times {10}^{-18}{\text{g cm s}}^{-1}$. The uncertainty in the velocity of the electron is:

(Mass of an electron is $9\times {10}^{-28}\text{g})$

If the speed of the particle is $v=4t^3+6\text{m/s}$, the distance of the particle as a function of time $t$ and the average speed in $3\text{sec}$ respectively are

For a particle in uniform circular motion the acceleration $\overrightarrow{a}$ at a point $P(R,\theta )$on the circle of radius R is (here $\theta$ is measured from the x-axis)

An athlete running with constant speed, completes one round of a circular track of radius $R$ in $40\text{seconds}$. What will be his angular displacement at the end of $20\text{seconds}$?

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A gun fires $10$ bullets/sec each of mass $10\text{gm}$, with a muzzle velocity of $50\text{m/s}$. Find the force required to hold the gun in position.

White light is used to illuminate the two slits in YDSE. The separation between the slits is b and the screen is at a distance d (>>b) from the slits. At a point on the screen directly in front of one of the slits, certain wavelengths are missing. Some of these missing wavelengths are

A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern is formed on a screen placed perpendicular to the direction of the incident beam. At the first minimum of the diffraction pattern, the phase difference between the rays coming from the two edges of the slit is

Two metallic slabs of same area of cross section and length having thermal conductivities $300{\text{W/m}}^{\circ }\text{C}$ and $200{\text{W/m}}^{\circ }\text{C}$ respectively are connected in series combination. Find the equivalent thermal conductivity (in ${\text{W/m}}^{\circ }\text{C}$)

What is equavent weight means in firaday 2 law