Find the dimensions of a and b in the formula \(\left[ P+{{a\over V^2}} \right][V-b]=RT\) where P is pressure and V is the volume of the gas

Two vectors \(\vec A\) and \(\vec B\) of magnitude 5 units and 7 units make an angle 60° with each other. Find the magnitude of the difference vector \(\vec A\) - \(\vec B\) and its direction with respect to the vector \(\vec A\).

Show that impulse is the change of momentum.

A body of mass m is attached to the spring which is elongated to 25 cm by an applied force from its equilibrium position.
(a) Calculate the potential energy stored in the spring-mass system?
(b) What is the work done by the spring force in this elongation?
(c) Suppose the spring is compressed to the same 25 cm, calculate the potential energy stored and also the work done by the spring force during compression. (The spring constant, k= 0.1 N m^-1).

What is the difference between sliding and slipping?

A student was asked a question ‘why are there summer and winter for us? He replied as since Earth is orbiting in an elliptical orbit, when the Earth is very far away from the Sun(aphelion) there will be winter, when the Earth is nearer to the Sun(perihelion) there will be winter. Is this answer correct? If not, what is the correct explanation for the occurrence of summer and winter?

If excess pressure is balanced by a column of oil (with specific gravity 0.8) 4 mm high, where R = 2.0 cm, find the surface tension of the soap bubble.

500 g of water is heated from 30°C to 60°C. Ignoring the slight expansion of water, calculate the change in internal energy of the water? (specific heat of water 4184 J/kg.K)

Explain in detail the Maxwell Boltzmann distribution function.

Consider two springs with force constants 1 N m⁻¹ and 2 N m⁻¹ connected in parallel. Calculate the effective spring constant (k_p) and comment on k_p.