Unit And Dimensions Set-1

Q1: The unit of impulse is the same as that of

Q2: Which of the following is not the unit of energy?

Q3: If $a$ and $b$ are two physical quantities having different dimensions then which of the following can denote a new physical quantity?

Q4: The time dependence of a physical quantity $P = P_0 \exp(-\alpha t^2)$ where $\alpha$ is a constant and $t$ is time. The constant $\alpha$

Q5: Which pair of following quantities has dimensions different from each other?

Q6: The product of energy and time is called action. The dimensional formula for action is same as that for

Q7: What is the physical quantity whose dimensions are $[M L^2 T^{-2}]$?

Q8: If $E, M, J$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively, then $\frac{E J^2}{M^5 G^2}$ has the dimensions of

Q9: The position of a particle at time $t$ is given by $x(t) = \frac{V_0}{\alpha} (1 - e^{-\alpha t})$ where $V_0$ is a constant and $\alpha > 0$. The dimensions of $V_0$ and $\alpha$ are respectively.

Q10: If force $F$ is given by $F = P t^{-1} + \alpha t$, where $t$ is time. The unit of $P$ is same as that of

Q11: When a wave traverses a medium, the displacement of a particle located at $x$ at time $t$ is given by $y = a \sin(bt - cx)$ where $a, b$ and $c$ are constants of the wave. The dimensions of $b$ are the same as those of

Q12: In a book, the answer for a particular question is expressed as $b = \frac{m a}{k} \left[ \sqrt{1 + \frac{2 k l}{m a}} \right]$ here $m$ represents mass, $a$ represents acceleration, $l$ represents length. The unit of $b$ should be

Q13: If the units of mass and length are doubled then the unit of kinetic energy will become

Q14: The least count of a stop watch is 0.2 second. The time of 20 oscillations of a pendulum is measured to be 25 seconds. The percentage error in the time period is

Q15: The dimensions of a cuboidal block measured with a vernier callipers having least count of 0.1 mm is 5 mm $\times$ 10 mm $\times$ 5 mm. The maximum percentage error in measurement of volume of the block is

Q16: In an experiment the quantities $x, y$ and $z$ are measured. Then $i$ is calculated from the data as $i = \frac{x^2 y}{z^2}$. If percentage errors in $x, y$ and $z$ are respectively 1%, 3%, 2%, then percentage error in $i$ is:

Q17: The external and internal diameters of a hollow cylinder are measured to be $(4.23 \pm 0.01)$ cm and $(3.89 \pm 0.01)$ cm. The thickness of the wall of the cylinder is

Q18: Two resistors $R_1 = (24 \pm 0.5) \Omega$ and $R_2 = (8 \pm 0.3) \Omega$ are joined in series. The equivalent resistance is

Q19: The pitch of a screw gauge is 0.5 mm and there are 100 divisions on its circular scale. The instrument reads +2 divisions when nothing is put in-between its jaws. In measuring the diameter of a wire, there are 8 divisions on the main scale and 83rd division coincides with the reference line. Then the diameter of the wire is

Q20: The smallest division on the main scale of a vernier callipers is 1 mm, and 10 vernier divisions coincide with 9 main scale divisions. While measuring the diameter of a sphere, the zero mark of the vernier scale lies between 2.0 and 2.1 cm and the fifth division of the vernier scale coincides with a mark on main scale. Then diameter of the sphere is

Q21: For a satellite orbiting around the Earth, its orbital velocity $v_0$ is found to depend on mass of Earth $M$, radius of earth $R$ and universal gravitational constant $G$. The orbital velocity is proportional to

Q22: The vernier constant of a vernier callipers is 0.1 mm and it has zero error of $-0.05$ cm. While measuring the diameter of a sphere, the main scale reading is 1.7 cm and coinciding vernier division is 5. The correct diameter will be $n \times 10^{-2}$ cm. Find $n$

Q23: In a particular system, the unit of length, mass and time are chosen to be 10 cm, 10g and 0.1s respectively. The unit of force in this system will be equal to

Q24: In sub-atomic physics, one often associates a characteristic wavelength $\lambda$ with a particle of mass $m$. If $\hbar = \frac{h}{2\pi}$ ($h$ being Planck's constant) and $c$ is the speed of light, which of the following expression is most likely to be correct one?

Q25: If the mass, time and energy are taken as fundamental physical quantities then dimensional formula of length is

Q26: Given that $\ln(\alpha / p \beta) = \alpha z / k_B \theta$ where $p$ is pressure, $z$ is distance, $k_B$ is Boltzmann constant and $\theta$ is temperature. The dimensions of $\beta$ are

Q27: Let $y = l^2 - \frac{l^3}{z}$ where $l = 2.0 \pm 0.1$, $z = 1.0 \pm 0.1$, then the value of $y$ is given by

Q28: The time periods of a pendulum are measured to be $T_1 = 8.01$ s and $T_2 = 8.41$ s by a student who used stop watch having least count = 0.01 sec, then the best reported measurement of time period (in sec) is

Q29: A gas bubble from an explosion under water oscillates with period $T$ proportional to $p^a d^b E^c$, where $p$ is static pressure, $d$ is the density of water, $E$ is the total energy of the explosion. The values of $a, b, c$ respectively will be

Q30: Electric field in a certain region is given by $\vec{E} = \left( \frac{A}{x^2} + \frac{B}{y^2} \right)$. The SI unit of $A$ and $B$ are: