Advertisements
Advertisements
Question
Suggest a way to measure the distance between the sun and the moon.
Solution
The distance between the Sun and the Moon can be measured using the Pythagoras theorem when the Earth makes an angle of 90° with the Sun and the Moon. We already know the distances from the Sun to the Earth and from the Earth to the Moon. However, these distances keep changing due to the revolution of the Moon around the Earth and the revolution of the Earth around the Sun.
APPEARS IN
RELATED QUESTIONS
It is often said that the world is witnessing now a second industrial revolution, which will transform the society as radically as did the first. List some key contemporary areas of science and technology, which are responsible for this revolution.
Write in about 100 words a fiction piece based on your speculation on the science and technology of the twenty-second century.
Attempt to formulate your ‘moral’ views on the practice of science. Imagine yourself stumbling upon a discovery, which has great academic interest but is certain to have nothing but dangerous consequences for the human society. How, if at all, will you resolve your dilemma?
Science, like any knowledge, can be put to good or bad use, depending on the user.Given below are some of the applications of science. Formulate your views on whether the particular application is good, bad or something that cannot be so clearly categorized :
(a) Mass vaccination against smallpox to curb and finally eradicate this disease from the population. (This has already been successfully done in India.)
(b) Television for the eradication of illiteracy and for mass communication of news and ideas.
(c) Prenatal sex determination.
(d) Computers for the increase in work efficiency.
(e) Putting artificial satellites into orbits around the Earth.
(f) Development of nuclear weapons.
(g) Development of new and powerful techniques of chemical and biological warfare.
(h) Purification of water for drinking.
(i) Plastic surgery.
(j) Cloning.
Suppose you are told that the linear size of everything in the universe has been doubled overnight. Can you test this statement by measuring sizes with a metre stick? Can you test it by using the fact that the speed of light is a universal constant and has not changed? What will happen if all the clocks in the universe also start running at half the speed?
Find the dimensions of electric dipole moment p .
The defining equations are p = q.d and M = IA;
where d is distance, A is area, q is charge and I is current.
Find the dimensions of magnetic dipole moment M.
The defining equations are p = q.d and M = IA;
where d is distance, A is area, q is charge and I is current.
A particle moves on a given straight line with a constant speed ν. At a certain time it is at a point P on its straight line path. O is a fixed point. Show that \[\vec{OP} \times \vec{\nu}\] is independent of the position P.
The force on a charged particle due to electric and magnetic fields is given by \[\vec{F} = q \vec{E} + q \vec{\nu} \times \vec{B}\].
Suppose \[\vec{E}\] is along the X-axis and \[\vec{B}\] along the Y-axis. In what direction and with what minimum speed ν should a positively charged particle be sent so that the net force on it is zero?
The electric current in a discharging R−C circuit is given by i = i0 e−t/RC where i0, R and C are constant parameters and t is time. Let i0 = 2⋅00 A, R = 6⋅00 × 105 Ω and C = 0⋅500 μF. (a) Find the current at t = 0⋅3 s. (b) Find the rate of change of current at at 0⋅3 s. (c) Find approximately the current at t = 0⋅31 s.
Find the area bounded under the curve y = 3x2 + 6x + 7 and the X-axis with the ordinates at x = 5 and x = 10.
Find the area enclosed by the curve y = sin x and the X-axis between x = 0 and x = π.
Find the area bounded by the curve y = e−x, the X-axis and the Y-axis.
A rod of length L is placed along the X-axis between x = 0 and x = L. The linear density (mass/length) ρ of the rod varies with the distance x from the origin as ρ = a + bx. (a) Find the SI units of a and b. (b) Find the mass of the rod in terms of a, b and L.
A metre scale is graduated at every millimetre. How many significant digits will be there in a length measurement with this scale?
