Question

Two blocks are connected by a string as shown in the diagram. The upper block is hung by another string. A force F applied on the upper string produces an acceleration of $2 m / s ^ { 2 }$ in the upward direction in both the blocks. If T and $T ^ { \prime }$ be the tensions in the two parts of the string, then

• A. $T = 70.8 N$ and $T ^ { \prime } = 47.2 \mathrm {~N}$
• B. $T = 58.8 \mathrm {~N}$ and $T ^ { \prime } = 47.2 \mathrm {~N}$
• C. $T = 70.8 N$ and $T ^ { \prime } = 58.8 \mathrm {~N}$
• D. $T = 70.8 N$ and $T ^ { \prime } = 0$

Answer 1

Answer: (A)

$T = 70.8 N$ and $T ^ { \prime } = 47.2 \mathrm {~N}$

Answer 2

From F.B.D. of mass 4 kg $4 a = T ^ { \prime } - 4 g$ .….(i)

From F.B.D. of mass 2 kg $2 a = T - T ^ { \prime } - 2 g$ .….(ii)

For total system upward force

$F = T = ( 2 + 4 ) ( g + a )$ $= 6 ( 18 + 2 ) N$ = 70.8 N

by substituting the value of T in equation (i) and (ii)

and solving we get $T ^ { \prime } = 47.2 \mathrm {~N}$