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

Given below are two statements : One is labelled as Assertion (A) and other is labelled as Reason (R).

Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is $$\rho$$ and radius of the drop is r, then $$\mathrm{T}=\mathrm{K} \sqrt{\rho \mathrm{r}^{3} / \mathrm{S}^{3 / 2}}$$ is dimensionally correct, where K is dimensionless.

Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period.

In the light of above statements, choose the correct answer from the options given below.

A
Both (A) and (R) are true and (R) is the correct explanation of (A)
B
Both (A) and (R) are true but (R) is not the correct explanation of (A)
C
(A) is true but (R) is false
D
(A) is false but (R) is true
2
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1

A travelling microscope has 20 divisions per $$\mathrm{cm}$$ on the main scale while its vernier scale has total 50 divisions and 25 vernier scale divisions are equal to 24 main scale divisions, what is the least count of the travelling microscope?

A
0.001 cm
B
0.002 mm
C
0.002 cm
D
0.005 cm
3
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
4
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 $$\beta$$.
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