Basic Maths and Units and Dimensions Questions

If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are

Figure below shows two paths that may be taken by a gas to go from a state A to a state C. In process AB, 400 J of heat is added to the system and in process BC, 100 J of heat is added to the system. ...

If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be :

A physical quantity of the dimensions of length that can be formed out of c, G and e24πε0is [c is velocity of light, G is universal constant of gravitation and e is charge] :-...

Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K1 and K2. The thermal conductivity of the composite rod will be :-...

Two blocks A and B of masses 3 m and m respectively are connected by a massless and 1nextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of accele...

An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current 'I along the same direction is shown in fig. Magnitude of force per unit length on the ...

A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water leve...

A block of mass m is placed on a smooth inclined wedge ABC of inclination θ as shown in the figure. The wedge is given an acceleration 'a' towards the right. The relation between a and &#...

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are KA, KB and KC respectively. AC is the major axis and SB is perpendicular to AC at the position of the...

A planet of radius R = × (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth on it and lower a wire of the same length and of linear mass density 10-3 kg m-1 into...

A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the figure. It is found that th...

A transparent slab of thickness d has a refractive index n (z) that increases with z. Here z is the vertical distance inside the slab, measured from the top. The slab is placed between two media with...

Two identical glass rods S1 and S2 (refractive index = 1.5) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance d as shown in the figure, with thei...

The dimensions of (μoεo) -1/2 are

The damping force on an oscillator is directly proportional to the velocity. The units of the constant ofproportionality are

The dimensions of (μ0ε0)-1/2 are

The inductance between A and D is

Identify the pair whose dimensions are equal

Which of the following pair of quantities do not have the same dimensions: