Basic Maths and Units and Dimensions Questions

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 particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x) = βx-2nwhere β and n are constants and x is the position of the particle. The acceler...

On observing light from three different stars P, Q and R, it was found that intensity of violet color is maximum in the spectrum of P, the intensity of green colour is maximum in the spectrum of R and...

The refracting angle of a prism is A, and refractive index of the material of the prism is cot(A/2). The angle of minimum deviation is :-

A ship A is moving Westwards with a speed of 10 km h-1 and a ship B 100 km South of A, is moving Northwards with a speed of 10 km h-1. The time after which the distance between them becomes shortest, ...

The approximate depth of an ocean is 2700 m. The compressibility of water is 45.4 × 10-11 Pa-1 anddensity of water is 103 kg/m3.What fractional compression of water will be obtained at the bottom...

A wind with speed 40 m/s blows parallel to the roof of a house. The area of the roof is 250 m2. Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on th...

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 :

The two ends of a metal rod are matainted at temperatures 100oC and 110oC. The rate of heat flow in the rod is found to be 4.0 J/s. If the ends are maintained at temperatures 200oC and 210oC, the rate...

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 :-...

Young's double slit experment is first performed in air and then in a medium other than air. It is found that 8th bright fringe in the medium lies where 5th dark fringe lies in air. The refractive...

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...

The x and y coordinates of the particle at any time are x = 5t - 2t2 and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2s is :-...

Two Polaroids P1 and P2 are placed with their axis perpendicular to each other. Unpolarised light I0 is incident on P1 . A third polaroid P3 is kept in between P1 and P2 such that its axis makes an an...

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...

An air column, closed at one end and open at the other, resonates with a tuning fork when the smallestlength of the column is 50 cm. The next larger length of the column resonating with the same tunin...