Principle of Homogeneity and Dimensional Consistency

JEE Main Physics · Units and Dimensions · 17 questions, latest first

• The potential energy of a particle changes with distance x from a fixed origin as V=(A √x)/(x+B), where A and B are constant with…20266 April, Shift 1 · Q27
• Consider a modified Bernoulli equation. (P+A/(B t^2))+ρ g(h+B t)+1/2 ρ V^2= constant If t has the dimension of time then the…202621 January, Shift 1 · Q26
• The equation for real gas is given by (P+a/V^2)(V-b)=R T, where P, V, T and R are the pressure, volume, temperature and gas…20252 April, Shift 1 · Q26
• The expression given below shows the variation of velocity (v) with time (t), v=At^2+Bt/(C+t). The dimension of ABC is:202529 January, Shift 1 · Q27
• The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light,…202524 January, Shift 2 · Q26
• The position of a particle moving on x -axis is given by x(t)=A sin t+B cos^2 t+C t^2+D, where t is time. The dimension of (A B…202523 January, Shift 1 · Q26
• The electric flux is φ=α σ+β λ where λ and σ are linear and surface charge density, respectively. ((α)/(β)) represents202523 January, Shift 1 · Q27
• What is the dimensional formula of a b^-1 in the equation (P+a/V^2)(V-b)=R T, where letters have their usual meaning.20245 April, Shift 2 · Q31
• Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational…20244 April, Shift 2 · Q32
• The equation of stationary wave is: y=2 a sin ((2 π nt)/(λ)) cos ((2 π x)/(λ)). Which of the following is NOT correct:20244 April, Shift 1 · Q31
• Consider two physical quantities A and B related to each other as E=(B-x^2)/(A t) where E, x and t have dimensions of energy,…202431 January, Shift 2 · Q31
• A force is represented by F=a x^2+b t^(1/2) where x= distance and t= time. The dimensions of b^2 / a are:202431 January, Shift 1 · Q31
• The equation of state of a real gas is given by (P+a/V^2)(V-b)=R T, where P, V and T are pressure, volume and temperature…202427 January, Shift 2 · Q31
• In the equation [X+a/Y^2][Y-b]=R T, X is pressure, Y is volume, R is universal gas constant and T is temperature. The physical…202313 April, Shift 2 · Q31
• (P+a/V^2)(V-b)=R T represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature…20231 February, Shift 1 · Q1
• Electric field in a certain region is given by E=(A/x^2 i+B/y^3 j). The SI unit of A and B are:202330 January, Shift 1 · Q1
• The equation of a circle is given by x^2+y^2=a^2, where a is the radius. If the equation is modified to change the origin other…202329 January, Shift 2 · Q1