1
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1

In an experiment to find out the diameter of wire using screw gauge, the following observations were noted :

(A) Screw moves $$0.5 \mathrm{~mm}$$ on main scale in one complete rotation

(B) Total divisions on circular scale $$=50$$

(C) Main scale reading is $$2.5 \mathrm{~mm}$$

(D) $$45^{\text {th }}$$ division of circular scale is in the pitch line

(E) Instrument has 0.03 mm negative error

Then the diameter of wire is :

A
2.92 mm
B
2.54 mm
C
2.98 mm
D
3.45 mm
2
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1

Consider the efficiency of carnot's engine is given by $$\eta=\frac{\alpha \beta}{\sin \theta} \log_e \frac{\beta x}{k T}$$, where $$\alpha$$ and $$\beta$$ are constants. If T is temperature, k is Boltzmann constant, $$\theta$$ is angular displacement and x has the dimensions of length. Then, choose the incorrect option :

A
Dimensions of $$\beta$$ is same as that of force.
B
Dimensions of $$\alpha^{-1} x$$ is same as that of energy.
C
Dimensions of $$\eta^{-1} \sin \theta$$ is same as that of $$\alpha \beta$$.
D
Dimensions of $$\alpha$$ is same as that of $$\beta$$.
3
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

The dimensions of $$\left(\frac{\mathrm{B}^{2}}{\mu_{0}}\right)$$ will be :

(if $$\mu_{0}$$ : permeability of free space and $$B$$ : magnetic field)

A
$$\left[\mathrm{M}\, \mathrm{L}^2 \,\mathrm{T}^{-2}\right]$$
B
$$\left[\mathrm{M} \,\mathrm{L} \,\mathrm{T}^{-2}\right]$$
C
$$\left[\mathrm{M} \,\mathrm{L}^{-1} \,\mathrm{~T}^{-2}\right]$$
D
$$\left[\mathrm{M} \,\mathrm{L}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]$$
4
JEE Main 2022 (Online) 27th July Evening Shift
+4
-1

An expression of energy density is given by $$u=\frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)$$, where $$\alpha, \beta$$ are constants, $$x$$ is displacement, $$k$$ is Boltzmann constant and t is the temperature. The dimensions of $$\beta$$ will be :

A
$$\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \theta^{-1}\right]$$
B
$$\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right]$$
C
$$\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\right]$$
D
$$\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{0}\right]$$
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