ques no 18 with explaination
ques no 18 with explaination 14. Which of the following is dimensionally inco 2 (I) u = v — at (4) v2 — u2 = 2as u2 = 2a (gt — 1) 15. 1 joule of energy is to be converted into new system of units in which length 10 metre, mass in 10 kg and time in 1 minute. The numerical value of I J in the new syste.n (2) 36 x 10-3 (1) 36 x 10-4 (4) 36 x 10-1 (3) 36 x 10-2 16. If the unit of force is 1 kilo newton, the length is 1 km, and time is 100 second what '"II be (1) 1000 kg (4) 100 kg (3) 10000 kg 17. The imensional formula for moment of couple is [ML2T-2] (3) [ML-1T-3] (2) [MLT-21 (4) [ML-2T-2] 18. The potential energy of a particle varies with distance x from a fixed origin as , where A and B are dimensional constants then dimensional formula for ABE 5,2+B (1) [ML7/2T-2] (3) [M2L9/2T-2] (2) [ML1112T-21 (4) [ML1312T-31 19. Of the following quantities which one has dimensions different from the remaining three?

Dear student

U = \frac{A \sqrt{x}}{x^{2} + B} . . . 1 1) A s x^{2} i s a d d e d t o B s o a s l i k e t e r m s h a s t h e s a m e d i m e n s i o n . d i m e n s i o n o f B = L^{2} 2) D i m e n s i o n o f d e n o m e n a t o r i s = L^{2} U = \frac{A \sqrt{x}}{x^{2} + B} U = \frac{A \sqrt{x}}{L^{2}} A = \frac{U \times L^{2}}{\sqrt{x}} A = \frac{M L^{2} T^{- 2} \times L^{2}}{\sqrt{L}} A = M L^{(4 - \frac{1}{2})} T^{- 2} A = M L^{\frac{7}{2}} T^{- 2} D i m e n s i o n o f A B = M L^{\frac{7}{2}} T^{- 2} \times L^{2} D i m e n s i o n o f A B = M L^{(\frac{7}{2} + 2)} T^{- 2} D i m e n s i o n o f A B = M L^{\frac{11}{2}} T^{- 2} R e g a r d s