Physical World

If the time period of the oscillation of a drop of liquid of density , radius , vibrating under surface tension is given by the formula It is observed that the time period is directly proportional to The value of should therefore be :

From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is :

In terms of resistance and time , the dimensions of ratio of the permeability and permittivity is :

If the capacitance of a nanocapacitor is measured in terms of a unit made by combining the electronic charge , Bohr radius , Planck's constant and speed of light then :

A screw gauge with a pitch of and a circular scale with divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is and the division coincides with the main scale line ?

A student measures the time period of oscillations of a simple pendulum four times. The data set is and . If the minimum division in the measuring clock is , then the reported mean time should be :

and are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation ln holds true. Then which of the combination is not a meaningful quantity ?

A physical quantity is described by the relation If the relative errors in the measurement of and respectively, are and , then the relative error in will be :

In a screw gauge, complete rotations of the screw cause it to move a linear distance of . There are circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of main scale divisions and circular scale divisions. Assuming negligible zero error, the thickness of the wire is :

If speed , acceleration and force are considered as fundamental units, the dimension of Young's modulus will be :

In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for oscillations is measured by using a watch of second least count. The mean value of time taken comes out to be . The length of pendulum is measured by using a meter scale of least count and the value obtained is . The percentage error in the determination of is close to :

The density of a material in SI units is . In certain units in which the unit of length is and the unit of mass is , the numerical value of density of the material is :

Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is:

If speed , area and force are chosen as fundamental units, then the dimension of Young's modulus will be :

A screw gauge has divisions on its circular scale. The circular scale is units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of is noticed on the pitch scale. The nature of zero error involved, and the least count of the screw gauge, are respectively :

The quantities and are defined where C - capacitance R - Resistance, l - length, E - Electric field, B - magnetic field and - free space permittivity and permeability respectively. Then :

Dimensional formula for thermal conductivity is (here denotes the temperature)

A quantity is given by in terms of moment of inertia force , velocity work and Length . The dimensional formula for is same as that of :

If momentum , area and time are taken to be the fundamental quantities then the dimensional formula for energy is :