Question

Three blocks M1, M2, M3 having masses 4 kg, 6 kg and 10 kg respectively are hanging from a smooth pully using rope 1, 2 and 3 as shown in figure. The tension in the rope 1, T1 when they are moving upward with acceleration of 2ms–2 is ............... N (if g = 10 m/s2 )

Answer 1

Let’s analyze the forces acting on each block.

For the system as a whole (masses $M_1$, $M_2$, and $M_3$ together) moving upwards with an acceleration $a = 2 \, \mathrm{m/s^2}$:

Total mass, $M = M_1 + M_2 + M_3 = 4 + 6 + 10 = 20 \, \mathrm{kg}.$

Total weight, $W = Mg = 20 \times 10 = 200 \, \mathrm{N}$

Since the entire system is accelerating upwards, the net force $F$ required to produce this acceleration is given by:

$F = Ma = 20 \times 2 = 40 \, \mathrm{N}$

Thus, the tension $T_1$ in rope 1 must support both the weight and the additional force required for acceleration:

$T_1 = W + F = 200 + 40 = 240 \, \mathrm{N}$