Units and Dimensions

Q.

What are supplementary quantities?

Q. A light-year is a unit of

1. time
2. mass
3. distance
4. energy

Q. RMS speed of molecules of gas A at temperature T1 is v and that of molecules of gas B at temperature T2 is 2v. Then which of the following is necessarily true? Options: 1)T2 = 2T1 2)T2 < T1 3)T2 > T1 4)None of these

Q. a charged particle of mass m and charge q enters into a magnetic field B with a velocity v at an angle theta with B. choose the incorrect option. a) the kinetic energy of particle will not change if theta is not equal to0. b)momentum of the particle will not change if theta is not equal to 0 c)the particle movves in a circle of radius mv/qv if theta equals 90

Q.

A weightless thread can support tension upto 30 N. A stone of mass 0.5 kg is tied to it and is revolved in a circular path of radius 2 m in a vertical plane. If g= 10m/$s^2$ , then the maximum angular velocity of the stone will be

1. 

2. 

3. 

4. 

Q.

A cup of tea cools from ${80}^{o}C$ to ${60}^{o}C$ in one minute. The ambient temperature is ${30}^{o}C$. In cooling from ${60}^{o}C$ to ${50}^{o}C$ it will take

1. 

2. 

3. 

4. 

Q.

$N{m}^2/k{g}^2$ is the SI unit of___

Q. If $u_1$ and $u_2$ are the units selected in two systems of measurement and $n_1$ and $n_2$ are their numerical values respectively, then for constant physical quantity

1. $n_1{u}_1=n_2{u}_2$
2. $n_1{u}_1+n_2{u}_2=0$
3. $n_1{n}_2=u_1{u}_2$
4. $n_1+u_1=n_2+u_2$

Q. If the dimensions of a physical quantity are given by $\left[M^a{L}^b{T}^c\right]$, then the physical quantity will be

1. velocity if $a=1,b=0,c=-1$
2. acceleration if $a=1,b=1,c=-2$
3. force if $a=0,b=-1,c=-2$
4. pressure if $a=1,b=-1,c=-2$

Q. A great physicist of this century (P.A.M. Dirac) loved playing with numerical values of Fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics (c, e, mass of electron, mass of proton) and the gravitational constant G, he could arrive at a number with the dimension of time. Further, it was a very large number, its magnitude being close to the present estimate on the age of the universe (~15 billion years). From the table of fundamental constants in this book, try to see if you too can construct this number (or any other interesting number you can think of ). If its coincidence with the age of the universe were significant, what would this imply for the constancy of fundamental constants?

Q. Show that the angular momentum about any point of a single particle moving with constant velocity remain constant throughout the motion. Is there any external torque on the particle

Q. 57. how numerical value is inversely proportional to its unit

Q.

A sphere of radius r is kept on a concave mirror of radius of curvature R. The arrangement is kept on a horizontal table (the surface of concave mirror is frictionless and sliding not rolling). If the sphere is displaced from its equilibrium position and left, then it executes S.H.M. The period of oscillation will be

1. 

2. 

3. 

4. 

Q. If impulse I varies with time t as I=20t^2-40t.The change in momentum is minimum at -t=2s -t=1/2s -t=1s -t=3/2

Q. Which of the following represents the correct dimensions of the gravitational constant?

1. $\left[M^{-1}{L}^3{T}^{-2}\right]$
2. $\left[ML{T}^{-1}\right]$
3. $\left[M{L}^{-1}{T}^{-2}\right]$
4. $\left[M{L}^{-2}{T}^{-2}\right]$

Q. In equation, $r=m^2\sin \left(\pi t\right)$, where $t$ represents time. If the unit of $m$ is $\text{N}$, then the unit of $r$ is

1. $\text{N}$
2. ${\text{N}}^2$
3. $\text{N}s$
4. ${\text{N}}^{2}s$

Q. Hertz is the unit for

1. Frequency
2. Force
3. Electric charge
4. Velocity

Q. The displacement of a body at a particular second $\left(n\right)$ is given by the expression $s_{n^{th}}=u+\frac{a}{2}(2n-1)$. The dimensional formula of $s_{n^{th}}$ in this equation is

1. $\left[M^1{L}^1{T}^0\right]$
2. $\left[M^0{L}^1{T}^{-1}\right]$
3. $\left[M^0{L}^1{T}^0\right]$
4. $\left[M^0{L}^0{T}^0\right]$

Q. $\text{[M L T}{}^{-1}\text{]}$ is dimensional formula of

1. Power
2. Momentum
3. Force
4. Couple

Q.

An electric lamp is marked$220V,100W$. It is used for $5$hours. Calculate the total energy consumed by the lamp in $KWh$.

Q. A dimensionless quantity
(a) never has a unit,
(b) always has a unit,
(c) may have a unit,
(d) does not exist.

Q. Time varying Torque 8t N m is applied on an objectabout pivot. Angular momentum of body attime t 2 s is

Q. Which of the following is not the name of a physical quantity?

1. meter
2. impulse
3. energy
4. density

Q. How to find relative velocity of rain with respect to man if rain is already falling at an angle theta with the vertical

Q. Q. rain is falling at a speed of 25 root 3 m/s vertically .the wind blows at a speed of 25 m/s from west to east. find the velocity of rain as experienced by a person standing on the ground.

Q. 1 metre long tube closed at both ends is lying horizontally a Mercury column of length 0.1 metre is filled in its middle and in rest two parts air is filled at atmospheric pressure what will be the displacement of the Mercury column when the two is turned to vertical position atmospheric pressure equals to 0.76 mm of Hg

Q. 2 blocks of mass 2kg and 4kg tied to a string passing over a frictionless pulley. What will be the magnitude of accelaration of masses when they are allowed to move freely

Q. Which of the following is not a fundamental physical quantity?

1. Mass
2. Length
3. Temperature
4. Density

Q. a car 2m long travelling at 30m/s overtakes another car 4m long travelling at 20m/s.the time taken by the first car to pass the second car is

Q. 68. Two strings of length l=0.5m each are connected to a block of mass m=2 kg at one end and their ends are attached to the point A and B 0.5 m apart on a vertical pole which rotates with a constant angular velocity w=7rad/s .find the ratio T1/T2 of tension in the upper string (T1) and the lower string(T2).(Use g=9.8m/s2