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 . The value of AB will be:
1. (0.25 0.08) m
2. (0.25 0.5) m
3. (0.25 0.05) m
4. (0.25 0.135) m
You measure two quantities as A = 1.0 m 0.2 m, B = 2.0 m 0.2 m. We should report the correct value for as
1. 1.4 m 0.4 m
2. 1.41 m 0.15 m
3. 1.4 m 0.3 m
4. 1.4 m 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 the 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) \(y = \left({\dfrac a T}\right) \sin \left({\dfrac t a}\right)\)
(d) \(y = a \sqrt 2 \left(\sin \left({\dfrac {2 \pi t} T}\right) - \cos \left({\dfrac {2 \pi t} T}\right)\right)\)
(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 – /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, where 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)