1
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity X as follows: [position] = [X$$\alpha$$]; [speed] = [X$$\beta$$ ]; [acceleration] = [Xp]; [linear momentum] = [Xq]; [force] = [Xr]. Then
A
$$\alpha$$ + p = 2$$\beta$$
B
p + q - r = $$\beta$$
C
p - q + r = $$\alpha$$
D
p + q + r = $$\beta$$
2
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L, which of the following statement(s) is/are correct?
A
The dimension of force is [L]-3
B
The dimension of power is [L]-5
C
The dimension of energy is [L]-2
D
The dimension of linear momentum is [L]-1
3
JEE Advanced 2016 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic motion is $$T = 2\pi \sqrt {{{7\left( {R - r} \right)} \over {5g}}}$$. The values of R and r are measured to be (60 $$\pm$$ 1) mm and (10 $$\pm$$ 1) mm, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s, 0.57 s, 0.54 s and 0.59 s. The least count of the watch used for the measurement of time period is 0.01 s. Which of the following statement(s) is(are) true?
A
The error in the measurement of r is 10 %
B
The error in the measurement of T is 3.57 %
C
The error in the measurement of T is 2 %
D
The error in the determined value of g is 11 %
4
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+3
-1
A length-scale (l) depends on the permittivity ($$\varepsilon$$) of a dielectric material, Boltzmann constant (kB), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried by each of the particles. Which of the following expression(s) for I is(are) dimensionally correct?
A
$$l = \sqrt {\left( {{{n{q^2}} \over {\varepsilon {k_b}T}}} \right)}$$
B
$$l = \sqrt {\left( {{{\varepsilon {k_b}T} \over {n{q^2}}}} \right)}$$
C
$$l = \sqrt {\left( {{{{q^2}} \over {\varepsilon {n^{2/3}}{k_B}T}}} \right)}$$
D
$$l = \sqrt {\left( {{{{q^2}} \over {\varepsilon {n^{1/3}}{k_B}T}}} \right)}$$
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