Statement I: In the lac operon, the z gene does indeed code for β-galactosidase, the enzyme that hydrolyzes lactose into galactose and glucose. This statement is true.
Statement II: The lac operon is induced by the presence of lactose (or allolactose, a lactose isomer). The presence of glucose actually represses the lac operon, even if lactose is present. This phenomenon is called catabolite repression. Galactose doesn’t directly induce the lac operon; it’s the presence of lactose that matters. Therefore, statement II is false.
A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point P making an angle \( \theta \) from the horizontal, the ratio of the speed \(v\) of the bob at point P to its initial speed \(v_0\) is :