Every question from past board papers on Physics and Measurement, newest paper first. Open any question for its full worked answer.
A physical quantity \(P\) is related to four observations \(a\), \(b\), \(c\) and \(d\) as follows:
\(P = a^3b^2 / c\sqrt{d}\)
The percentage errors of measurement in \(a\), \(b\), \(c\) and \(d\) are 1%, 3%, 2%, and 4% respectively. The percentage error in the quantity \(P\) is
The quantities which have the same dimensions as those of solid angle are :
A force defined by \(F=\alpha t^2+\beta t\) acts on a particle at a given time \(t\). The factor which is dimensionless, if \(\alpha\) and \(\beta\) are constants, is:
A metal wire has mass \((0.4\pm0.002)\) g, radius \((0.3\pm0.001)\) mm and length \((5\pm0.02)\) cm. The maximum possible percentage error in the measurement of density will nearly be:
The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are :
The dimensions \([\text{MLT}^{-2}\text{A}^{-2}]\) belong to the :
Plane angle and solid angle have :
Match List - I with List - II :
List - I: (a) Gravitational constant (G) (b) Gravitational potential energy (c) Gravitational potential (d) Gravitational intensity
List - II: (i) \([L^{2}T^{-2}]\) (ii) \([M^{-1}L^{3}T^{-2}]\) (iii) \([LT^{-2}]\) (iv) \([ML^{2}T^{-2}]\)
Choose the correct answer from the options given below :
The area of a rectangular field (in \(\text{m}^2\)) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is :
If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.
If E and G respectively denote energy and gravitational constant, then \(\frac{E}{G}\) has the dimensions of :
The energy required to break one bond in DNA is \(10^{-20}\) J. This value in eV is nearly :
Dimensions of stress are :
Taking into account of the significant figures, what is the value of 9.99 m \(-\) 0.0099 m ?
In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where \(X = \frac{A^2 B^{1/2}}{C^{1/3} D^3}\), will be :
A physical quantity of the dimensions of length that can be formed out of \(c\), G and \(\frac{e^2}{4\pi\epsilon_0}\) is [\(c\) is velocity of light, G is universal constant of gravitation and e is charge] :
Planck's constant (\(h\)), speed of light in vacuum (\(c\)) and Newton's gravitational constant (\(G\)) are three fundamental constants. Which of the following combinations of these has the dimension of length?
