JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Laws of Motion

Three blocks A, B and C are pulled on a horizontal smooth surface by a force of 80 N as shown in figure

The tensions

T_{1}

and

T_{2}

in the string are respectively:

(A) $40 N, 64 N$ ✓ Correct
(B) $60 N, 80 N$
(C) $88 N, 96 N$
(D) $80 N, 100 N$

Answer: (A)

Solution

Blocks A (5 kg), B (3 kg) and C (2 kg) are connected in a line and pulled together by a force of 80 N applied at C, with string tension

T_{1}

between A and B, and

T_{2}

between B and C.

The whole system accelerates together:

a = \frac{F}{m _{A} + m _{B} + m _{C}} = \frac{80}{5 + 3 + 2} = 8 m/s^{2}

For block A alone, the only horizontal force is

T_{1}

T_{1} = m_{A} a = 5 \times 8 = 40 N

For blocks A and B together, the only horizontal force is

T_{2}

T_{2} = (m_{A} + m_{B}) a = 8 \times 8 = 64 N

JEE Main · 2024 · 30 Jan 2024 · Shift 2 · Single correct option

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