Dimensions PYQs: JEE Mains Physics – Page 3

Showing 101–116 of 116 questions

101. 101. In \(SI\, units\), the dimensions of \(\sqrt {\frac{{{ \varepsilon _0}}}{{{\mu _0}}}} \) is 2019 Medium
102. 102. 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
103. 103. 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
104. 104. 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
105. 105. 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
106. 106. 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
107. 107. 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
108. 108. \(A, B, C\) 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
109. 109. 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
110. 110. 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
111. 111. 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
112. 112. 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
113. 113. 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
114. 114. 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
115. 115. 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
116. 116. The dimensions of angular momentum , latent heat and capacitance are, respectively. 2013 Hard

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