Which of the following pairs of physical quantities does not have the same dimensional formula?

1.	work and torque
2.	angular momentum and Planck's constant
3.	tension and surface tension
4.	impulse and linear momentum

The measure of two quantities along with the precision of respective measuring instrument is $\mathrm{A}=2.5{\mathrm{ms}}^{-1}\pm 0.5{\mathrm{ms}}^{-1}, \mathrm{B}=0.10\mathrm{s}\pm 0.01\mathrm{s}$. The value of AB will be:

1. (0.25 $\pm$ 0.08) m

2. (0.25 $\pm$ 0.5) m

3. (0.25 $\pm$ 0.05) m

4. (0.25 $\pm$ 0.135) m

You measure two quantities as A = 1.0 m $\pm$ 0.2 m, B = 2.0 m $\pm$ 0.2 m. We should report the correct value for $\sqrt{\mathrm{AB}}$ as

1. 1.4 m $\pm$ 0.4 m

2. 1.41 m $\pm$ 0.15 m

3. 1.4 m $\pm$ 0.3 m

4. 1.4 m $\pm$ 0.2 m

Which of the following measurement is most precise?
1. \(5.00\) mm
2. \(5.00\) cm
3. \(5.00\) m
4. \(5.00\) km

The mean length of an object is \(5~\text{cm}\). Which of the following measurements is most accurate?
1. \(4.9~\text{cm}\)
2. \(4.805~\text{cm}\)
3. \(5.25~\text{cm}\)
4. \(5.4~\text{cm}\)

Young's modulus of steel is \(1.9 \times 10^{11} \mathrm{~N} / \mathrm{m}^2\). When expressed in CGS units of \(\mathrm{dyne/cm^2}\), it will be equal to: \((1 \mathrm{~N}=10^5 \text { dyne, } 1 \mathrm{~m}^2=10^4 \mathrm{~cm}^2)\)
1. \( 1.9 \times 10^{10} \)
2. \( 1.9 \times 10^{11} \)
3. \( 1.9 \times 10^{12} \)
4. \( 1.9 \times 10^9\)

On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is/are not correct.
a. \(y = a\sin \left(2\pi t / T\right)\)
b. \(y = a\sin(vt)\)
c. \(y = \left({a \over T}\right) \sin \left({t \over a}\right)\)
d. \(y = a \sqrt 2 \left(\sin \left({2 \pi t \over T}\right) - \cos \left({2 \pi t \over T}\right)\right)\)
(Symbols have their usual meanings.)
Choose the correct option:
1. (a), (c)
2. (a), (b)
3. (b), (c)
4. (a), (d)

IF P, Q and R are physical quantities, having different dimensions, which of the following combination/s can never be a meaningful quantity?

(a) (P - Q)/R
(b) PQ - R
(c) PQ/R
(d) (PR - ${\mathrm{Q}}^2)$/R
(e) (R + Q)/P

Choose the correct option:

1. (a, e)

2. (a, d, e)

3. (a, c, d)

4. (b, d)

Photon is a quantum of radiation with energy E = h$\mathrm{\nu }$, where $\mathrm{\nu }$ is the frequency
and h is Planck's constant. The dimensions of h are the same as that of the following quantities.

(a) linear impulse

(b) angular impulse

(c) linear momentum

(d) angular momentum

Choose the correct option:

1. (a, d)

2. (b, d)

3. (c, d)

4. (a, b)