The operators for the total angular momentum and its three projections are ĵ and ſx , îy, ,, respectively. the commutator between two operators a and ể is [a, b] = âb - bâ. which of the following is true? (a) [j? , z]=0 () [,] = ini, (c) (1, ] = 0 (d) [1,1,] = ini, (e) [3, + i), j) = 0

In a system, when potential energy decreases, then entropy also decreases. true false

Agraduated cylinder contains 63.0 ml of water. a piece of gold, which has a density of 19.3 g/ cm3, is added to the water and the volume goes up to 64.5 ml. calculate the mass in grams of the gold that was added to the water. explain how you got your answer.

During the experiment if you could triple the breakaway magnetic force with all other quantities left unchanged, what is the new value for the critical velocity if it was v0 (initial velocity), initially? (b) now if you halved the radius with all other quantities left unchanged, what is the new critical velocity if it was v0 (initial velocity), initially? (c) if during the experiment, critical velocity quadrupled with all other quantities left unchanged, what is the new breakaway force if its magnitude was initially f0,?