1
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
A student determined Young's Modulus of elasticity using the formula $$Y = {{Mg{L^3}} \over {4b{d^3}\delta }}$$. The value of g is taken to be 9.8 m/s2, without any significant error, his observation are as following.

Physical
Quantity
Least count of the
Equipment used
for measurement

Observed value
Mass (M) 1 g 2 kg
Length of bar (L) 1 mm 1 m
Breadth of bar (b) 0.1 mm 4 cm
Thickness of bar (d) 0.01 mm 0.4 cm
Depression ($$\delta $$) 0.01 mm 5 mm

Then the fractional error in the measurement of Y is :
A
0.0083
B
0.0155
C
0.155
D
0.083
2
JEE Main 2021 (Online) 31st August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be :
A
[FT$$-$$1 V$$-$$1]
B
[FTV$$-$$1]
C
[FT2 V]
D
[FVT$$-$$1]
3
JEE Main 2021 (Online) 31st August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Match List - I with List - II.

List - I List - II
(a) Torque (i) MLT$$^{ - 1}$$
(b) Impulse (ii) MT$$^{ - 2}$$
(c) Tension (iii) ML$$^{ 2}$$T$$^{ - 2}$$
(d) Surface Tension (iv) MLT$$^{ - 2}$$


Choose the most appropriate answer from the option given below :
A
(a)-(iii), (b)-(i), (c)-(iv), (d)-(ii)
B
(a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
C
(a)-(i), (b)-(iii), (c)-(iv), (d)-(ii)
D
(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
4
JEE Main 2021 (Online) 31st August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Which of the following equations is dimensionally incorrect?

Where t = time, h = height, s = surface tension, $$\theta$$ = angle, $$\rho$$ = density, a, r = radius, g = acceleration due to gravity, v = volume, p = pressure, W = work done, T = torque, $$\in$$ = permittivity, E = electric field, J = current density, L = length.
A
$$v = {{\pi p{a^4}} \over {8\eta L}}$$
B
$$h = {{2s\cos \theta } \over {\rho rg}}$$
C
$$J = \in {{\partial E} \over {\partial t}}$$
D
$$W = \Gamma \theta $$
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