Give reasons for the following —

(a) In a single movable pulley, the velocity ratio is always more than the mechanical advantage.

(b) The efficiency of a movable pulley is always less than 100%.

(c) In case of a block and tackle system, the mechanical advantage increases with the increase in the number of pulleys.

(d) The lower block of a block and tackle pulley system must be of negligible weight.

(a) For an actual single movable pulley, due to (i) friction in the pulley bearings or at the axle and (ii) the weight of the pulley and string, the effort needed to lift up a load L will be more than $\dfrac{\text{L}}{2}$, so the mechanical advantage will be less than 2. But the velocity ratio will remain as 2. Hence, for a single movable pulley, the velocity ratio is always more than the mechanical advantage.

(b) As some effort is wasted in overcoming the friction between the strings and the grooves of the pulley as a result the efficiency of a movable pulley is always less than 100%.

(c) In the case of a block and tackle system, the mechanical advantage increases with the increase in the number of pulleys.

$M.A. = \dfrac{Load}{Effort} \\[0.5em] M.A. = \dfrac{nT}{T} = n \\[0.5em]$

∴ M.A. = Total number of pulleys in both the blocks

(d) The lower block of a block and tackle pulley system must be of negligible weight as efficiency is reduced due to the weight of the lower block of the pulley.

$\eta = 1 - \dfrac{w}{nE} \\[0.5em]$

where, w is the total weight of the lower block along with the pulleys in it.