1
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
$$\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{0}\right]$$
2
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1

A torque meter is calibrated to reference standards of mass, length and time each with $$5 \%$$ accuracy. After calibration, the measured torque with this torque meter will have net accuracy of :

A
15%
B
25%
C
75%
D
5%
3
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

In a Vernier Calipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and $$4^{\text {th }}$$ Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to $$1 \mathrm{~mm}$$. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and $$6^{\text {th }}$$ Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be :

A
3.02 cm
B
3.06 cm
C
3.10 cm
D
3.20 cm
4
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

A screw gauge of pitch $$0.5 \mathrm{~mm}$$ is used to measure the diameter of uniform wire of length $$6.8 \mathrm{~cm}$$, the main scale reading is $$1.5 \mathrm{~mm}$$ and circular scale reading is 7 . The calculated curved surface area of wire to appropriate significant figures is :

[Screw gauge has 50 divisions on its circular scale]

A
6.8 cm2
B
3.4 cm2
C
3.9 cm2
D
2.4 cm2
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