Assertion : In $y=A\sin (\omega t-kx),$ $(\omega t-kx)$ is dimensionless.

Reason : Because dimension of $\omega =\left[M^0{L}^{0}T\right].$

 

1. If both the assertion and the reason are true and the reason is a correct explanation of the assertion
2. If both the assertion and reason are true but the reason is not a correct explanation of the assertion
3. If the assertion is true but the reason is false
4. If both the assertion and reason are false

Assertion : Radian is the unit of plane angle.

Reason : One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.

Choose any one of the following four responses :

(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(3) If assertion is true but reason is false.

(4) If the assertion and reason both are false

Assertion : A.U. is much bigger than Å.

Reason : A.U. stands for astronomical unit and Å stands from Angstrom.

Choose any one of the following four responses :

(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(2) If both assertion and reason are true but the reason is not the correct explanation of the assertion.

(3) If the assertion is true but the reason is false.

(4) If the assertion and reason both are false.

Assertion: When we change the unit of measurement of a quantity, its numerical value changes.

Reason: Smaller the unit of measurement smaller is its numerical value.

Choose any one of the following four responses :

(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(3) If assertion is true but reason is false.

(4) If the assertion and reason both are false.

Assertion: Dimensional constants are the quantities whose values are constant.

Reason : Dimensional constants are dimensionless.

Choose any one of the following four responses :

(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(3) If assertion is true but reason is false.

(4) If the assertion and reason both are false.

Assertion :The time period of a pendulum is given by the formula, $T=2\pi \sqrt{\text{l}/\text{g}}$.

Reason : According to the principle of homogeneity of dimensions, only that formula is correct in which the dimensions of L.H.S. is equal to dimensions of R.H.S.

Assertion :In the relation $f=\frac{1}{2l}\sqrt{\frac{T}{m},}$ where symbols have standard meaning, m represent linear mass density.

Reason : The frequency has the dimensions of inverse of time.

Choose any one of the following four responses :

(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(3) If the assertion is true but the reason is false.

(4) If the assertion and reason both are false.

Assertion: Avogadro number is the number of atoms in one gram mole.

Reason: Avogadro number is a dimensionless constant.

Choose any one of the following four responses :

(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(2) If both assertion and reason are true but reason is not the correct explanation of the assertion.

(3) If assertion is true but reason is false.

(4) If the assertion and reason both are false.

Assertion : The quantity $(1\text{}/\text{}\sqrt{{\mu }_0{\epsilon }_0})$ is dimensionally equal to velocity and numerically equal to velocity of light.

Reason : ${\mu }_0$ is permeability of free space and ${\epsilon }_0$ is the permittivity of free space.

The surface tension of a liquid is 70 dyne/cm. In MKS system its value is 

1. 70 N/m

2. 7 × 10^–2 N/m

3. 7 × 10³ N/m

4. 7 × 10² N/m