STD 11 - Units,dimensions and measurement PYQs: JEE Mains Physics – Page 5

Showing 201–236 of 236 questions

201. 201. The quantities \(\quad x=\frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}, y=\frac{E}{B}\) and \(z=\frac{l}{C R}\) are defined where \(C-\) capacitance \(R-\)Resistance, \(l-\)length, \(E-\)Electric field, \(B-\)magnetic field and \(\varepsilon_{0}, \mu_{0},\) -free space permittivity and permeability respectively. Then.... 2020 Hard
202. 202. If Surface tension \((S)\), Moment of Inertia \((I)\) and Planck’s constant \((h)\), were to be taken as the fundamental units, the dimensional formula for linear momentum would be 2019 Hard
203. 203. In a simple pendulum experiment for determination of acceleration due to gravity \((g)\), time taken for \(20\) oscillations is measured by using a watch of \(1\, second\) least count. The mean value of time taken comes out to be \(30\,s\). The length of pendulum is measured by using a meter scale of least count \(1\, mm\) and the value obtained is \(55.0\, cm\). The percentage error in the determination of \(g\) is close to  ........... \(\%\) 2019 Hard
204. 204. In \(SI\, units\), the dimensions of \(\sqrt {\frac{{{ \varepsilon _0}}}{{{\mu _0}}}} \) is 2019 Medium
205. 205. In the density measurement of a cube, the mass and edge length are measured as \((10.00 \pm 0.10)\,\,kg\,\) and \((0.10 \pm 0.01)\,\,m\,\) respectively. The error in the measurement of density is 2019 Hard
206. 206. Let \(l, r, c\) and \(v\) represent inductance, resistance, capacitance and voltage, respectively. The dimension of \(\frac {l}{rcv}\) in \(SI\,units\) will be 2019 Medium
207. 207. The density of a material in \(SI\, units\) is \(128\, kg\, m^{-3}\). In certain units in which the unit of length is \(25\, cm\) and the unit of mass \(50\, g\), the numerical value of density of the material is 2019 Medium
208. 208. The diameter and height of a cylinder are measured by a meter scale to be \(12.6 \pm 0.1\, cm\) and \(34.2  \pm  0.1\, cm\), respectively. What will be the value of its volume in appropriate significant figures? 2019 Medium
209. 209. The force of interaction between two atoms is given by \(F\, = \,\alpha \beta \,\exp \,\left( { - \frac{{{x^2}}}{{\alpha kt}}} \right);\) where \(x\) is the distance, \(k\) is the Boltzmann constant and \(T\) is temperature and \(\alpha \) and \(\beta \) are two constants. The dimension of \(\beta \) is 2019 Hard
210. 210. The formula \(X = 5YZ^2\),  \(X\) and \(Z\) have dimensions of capacitance and magnetic field respectively. What are the dimensions of \(Y\) in \(SI\) units? 2019 Hard
211. 211. 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 2019 Medium
212. 212. The pitch and the number of divisions, on the circular scale, for a given screw gauge are \(0.5\,mm\) and \(100\) respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies \(3\) divisions below the mean line. The readings of the main scale and the circular scale for a thin sheet, are \(5.5\,mm\) and \(48\) respectively, the thickness of this sheet is 2019 Hard
213. 213. Which of the following combinations has the dimension of electrical resistance ( \({ \varepsilon _0}\) is the permittivity of vacuum and \({\mu _0}\) is the permeability of vacuum) ? 2019 Medium
214. 214. In a screw gauge, \(5\) complete rotations of the screw cause it to move a linear distance of \(0.25\, cm\). There are \(100\) circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of \(4\) main scale divisions and \(30\) circular scale divisions . Assuming negligible zero error, the thickness of the wire is 2018 Medium
215. 215. The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants \(G, h\) and \(c\) . Which of the following correctly gives the Planck length? 2018 Hard
216. 216. The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively \(1.5\%\) and \(1\%\), the maximum error in determining the density is   ........ \(\%\) 2018 Easy
217. 217. The percentage errors in quantities \(P, Q, R\)  and \(S\)  are \(0.5\%,\,1\%,\,3\%\)  and  \(1 .5\%\) respectively in the  measurement of a physical quantity \(A\, = \,\frac{{{P^3}{Q^2}}}{{\sqrt {R}\,S }}\) . the maximum percentage error in the value of \(A\)  will be ........... \(\%\) 2018 Hard
218. 218. The relative error in the determination of the surface area of a sphere is \(\alpha \). Then the relative error in the determination of its volume is 2018 Hard
219. 219. A physical quantity \(p\) is described by the relation \(p\, = a^{1/2}\, b^2\, c^3\, d^{-4}\) If the relative errors in the measurement of \(a, b, c\) and \(d\) respectively, are \(2\% , 1\%, 3\%\) and \(5\%\), then the relative error in \(P\) will be ........... \(\%\) 2017 Medium
220. 220. The following observations were taken for determining surface tension \(T\) of water by capillary method: diameter of capillary, \(D= 1.25 \times 10^{-2}\; m\) rise of water, \(h=1.45 \times 10^{-2}\; m \)  Using \(g= 9.80 \;m/s^2\) and the simplified relation \(T = \frac{{rhg}}{2}\times 10^3 N/m\) , the possible error in surface tension is ........... \(\%\) 2017 Medium
221. 221. Time \((T)\), velocity \((C)\) and angular momentum \((h)\) are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be 2017 Hard
222. 222. \(A, B, C\) and \(D\) are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation \(AD = C\, ln\, (BD)\) holds true. Then which of the combination is not a meaningful quantity ? 2016 Hard
223. 223. A screw gauge with a pitch of \(0.5 \ mm\) and a circular scale with \(50\) divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that wen the two jaws of the screw gauge are brought in contact, the \(45^{th} \)division coincides with the main scale line and the zero of the main scale is barely visible. What is the thickness of the sheet (in \(mm\)) if the main scale reading is \(0.5\ mm\) and the \(25^{th}\) division coincides with the main scale line  2016 Medium
224. 224. A student measures the time period of \(100\) oscillations of a simple pendulum four times. The data set is  \(90\;s\) ,\(91\;s \), \(95\;s\) and \(92\;s\). If the minimum division in the  measuring clock is \(1\;s\), then the reported mean time should be 2016 Medium
225. 225. A beaker contains a fluid of density \(\rho \, kg / m^3\), specific heat \(S\, J / kg\,^oC\) and viscosity \(\eta \). The beaker is filled upto height \(h\). To estimate the rate of heat transfer per unit area \((Q / A)\) by convection when beaker is put on a hot plate, a student proposes that it should depend on \(\eta \,,\,\left( {\frac{{S\Delta \theta }}{h}} \right)\) and \(\left( {\frac{1}{{\rho g}}} \right)\) when \(\Delta \theta \) (in \(^oC\)) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for \((Q / A)\) is 2015 Hard
226. 226. Diameter of a steel ball is measured using a Vernier callipers which has divisions of \(0. 1\,cm\) on its main scale \((MS)\) and \(10\) divisions of its vernier scale \((VS)\) match \(9\) divisions on the main scale. Three such measurements for a ball are given as

     S.No.	\(MS\;(cm)\)	\(VS\) divisions
     \((1)\)	\(0.5\)	\(8\)
     \((2)\)	\(0.5\)	\(4\)
     \((3)\)	\(0.5\)	\(6\)

     If the zero error is \(- 0.03\,cm,\) then mean corrected diameter is  ........... \(cm\) 2015 Medium
227. 227. If electronic charge \(e\), electron mass \(m\), speed of light in vacuum \(c\) and Planck 's constant \(h\) are taken as fundamental quantities, the permeability of vacuum \(\mu _0\) can be expressed in units of 2015 Hard
228. 228. If the capacitance of a nanocapacitor is measured in terms of a unit \(u\) made by combining the electric charge \(e,\) Bohr radius \(a_0,\) Planck's constant \(h\) and speed of light \(c\) then 2015 Hard
229. 229. The period of oscillation of a simple pendulum is \(T=2\pi \sqrt {\frac{l}{g}} \). Measured value of \(L\) is \(20.0\; cm\) known to \(1\; mm\) accuracy and time for \(100\) oscillations of the pendulum is found to be \(90\ s\) using a wrist watch of \(1\; s\) resolution. The accuracy in the determination of \(g\) is   ........ \(\%\) 2015 Easy
230. 230. A student measured the length of a rod and wrote it as \(3.50\;cm\). Which instrument did he use to measure it? 2014 Medium
231. 231. An experiment is performed to obtain the value of acceleration due to gravity \(g\) by using a simple pendulum of length \(L\). In this experiment time for \(100\, oscillations\) is measured by using a watch of \(1\, second\) least count and the value is \(90.0\, seconds\). The length \(L\) is measured by using a meter scale of least count \(1\, mm\) and the value is \(20.0\, cm\). The  error in the determination of \(g\) would be  ........... \(\%\) 2014 Hard
232. 232. 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 2014 Hard
233. 233. In terms of resistance \(R\) and time \(T\), the dimensions of ratio \(\frac{\mu } {\varepsilon }\) of the permeability \(\mu \) and permittivity \(\varepsilon \)  is 2014 Hard
234. 234. If the time period \(t\) of the oscillation of a drop of liquid of density \(d\), radius \(r\), vibrating under surface tension \(s\) is given by the formula \(t = \sqrt {{r^{2b}}\,{s^c}\,{d^{a/2}}} \) . It is observed that the time period is directly proportional to \(\sqrt {\frac{d}{s}} \) . The value of \(b\) should therefore be 2013 Hard
235. 235. Let \([ {\varepsilon _0} ]\) denote the dimensional formula of the permittivity of vacuum. If \(M =\) mass, \(L=\) length, \(T =\) time and \(A=\) electric current, then: 2013 Medium
236. 236. The dimensions of angular momentum , latent heat and capacitance are, respectively. 2013 Hard

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