A negligibly small current is passed through a wire of length 15 m and uniform cross-section \( 6.0 × 10^{−7} m^{2},\) and its resistance is measured to be 5.0 Ω. What is the resistivity of the material at the temperature of the experiment?
What physical quantity is the same for X-rays of wavelength \(10^{−10} m\), red light of wavelength \(6800 Å\) and radio waves of wavelength \(500\ m\)?
A small telescope has an objective lens of focal length 144cm and an eyepiece of focal length 6.0cm. What is the magnifying power of the telescope?What is the separation between the objective and the eyepiece?
At room temperature (27.0 °C) the resistance of a heating element is 100 Ω. What is the temperature of the element if the resistance is found to be 117 Ω, given that the temperature coefficient of the material of the resistor is \(1.70 \times 10^{-4} °C^{-1}.\)
A person with a normal near point(25cm)using a compound microscope with an objective of focal length 8.0mm and an eyepiece of focal length 2.5cm can bring an object placed at 9.0mm from the objective in sharp focus. What is the separation between the two lenses? Calculate the magnifying power of the microscope.
A compound microscope consists of an objective lens of focal length 2.0cm and an eyepiece of focal length 6.25cm separated by a distance of 15cm. How far from the objective should an object be placed in order to obtain the final image at(a)the least distance of distinct vision (25cm), and(b)at infinity? What is the magnifying power of the microscope in each case?
A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line?
A battery of emf 10 V and internal resistance 3 Ω is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?
The storage battery of a car has an emf of 12 V. If the internal resistance of the battery is 0.4Ω, what is the maximum current that can be drawn from the battery?
Double-convex lenses are to be manufactured from a glass of refractive index 1.55, with both faces of the same radius of curvature. What is the radius of curvature required if the focal length is to be 20 cm?
A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is(a)a convex lens of focal length 20cm, and(b)a concave lens of focal length 16cm?
What is the focal length of a convex lens of a focal length of 30cm in contact with a concave lens of a focal length of 20cm? Is the system a converging or a diverging lens? Ignore the thickness of the lenses.
From the relation \(R = R_0A^{\frac{1}{3}}\), where \(R_0\) is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).