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question_answer1) The density of a material in SI unit is \[128\text{ }kg\,\,{{m}^{-\,3}}\]. In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is:
question_answer2) The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 \[\mu m\] diameter of a wire is:
question_answer3) In the density measurement of a cube, the mass and edge length are measured as \[\left( 10.00\pm 0.10 \right)kg\] and\[\left( 0.10\pm 0.01 \right)m\], respectively. The error in the measurement of density is:
question_answer4) The area of a square is\[5.29\,c{{m}^{2}}\]. The area (in\[c{{m}^{2}}\]) of 7 such squares taking into account the significant figures, is:
question_answer5) A student has measured the length of a wire equal to 0.04580 m. This value of length has the number of significant figures equal to
question_answer6) The period of revolution (T) of a planet moving round the sun in a circular orbit depends upon the radius (r) of the orbit, mass (M) of the sun and the gravitation constant (G). Then T is proportional to \[{{r}^{a}}\]. The value of a is
question_answer7) Error in the measurement of radius of a sphere is 1 %. Then maximum percentage error in the measurement of volume is
question_answer8) Position of a body with acceleration 'a' is given by \[x=k{{a}^{m}}{{t}^{n}},\] where t is time and k is numeric constant. Find the value of m.
question_answer9) The displacement of a particle moving along x-axis with respect to time t is \[x=at+b{{t}^{2}}-c{{t}^{3}}\]. The dimensions of c is \[L{{T}^{-x}}\]. The value of x is
question_answer10) Subtract 0.2 J from 7.26 J and express the result with correct number of significant figures.
question_answer11) Multiply 107.88 by 0.610 and express the result with correct number of significant figures.
question_answer12) The velocity of water waves (v) may depend on their wave length\[\lambda \], the density of water \[\rho \] and the acceleration due to gravity, g. The method of dimensions gives the relation between these quantities as \[{{v}^{2}}=k{{g}^{x}}{{\lambda }^{x}}.\] The value of x is (Here, k is a constant)
question_answer13) To determine the Young's modulus of a wire, the formula is \[Y=\frac{F}{A}\times \frac{L}{\Delta L}\]: where L = length, A = area of cross-section of the wire, \[\Delta L=\]change in length of the wire when stretched with a force F. The conversion factor to change it from CGS to MKS system is
question_answer14) Let Q denote the charge on the plate of a capacitor of capacitance C. The dimensional formula for \[\frac{{{Q}^{2}}}{C}\] is \[[M{{L}^{x}}{{T}^{-x}}]\]. Find the value of x.
question_answer15) If the error in the measurement of the volume of sphere is 6%, then the error (in percent) in the measurement of its surface area will be
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