JEE Main 2024 · Physics · Kinematics and Laws of Motion · hard

A block A of mass 2 kg lies on a smooth horizontal table. A light string tied to A passes over a smooth fixed pulley at the table edge, then goes…

Single correct option

A block

A

of mass

2\ \mathrm{kg}

lies on a smooth horizontal table. A light string tied to

A

passes over a smooth fixed pulley at the table edge, then goes down and around a light movable pulley that carries a block

B

of mass

4\ \mathrm{kg}

, and its other end is fixed to the ceiling (both hanging parts of the string are vertical). The tension in the string after the system is released is (

g=10\ \mathrm{m\,s^{-2}}

)

A. $20.0\ \mathrm{N}$
B. $16.0\ \mathrm{N}$
C. $10.0\ \mathrm{N}$
D. $13.3\ \mathrm{N}$

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Answer: (D) $13.3\ \mathrm{N}$

The movable pulley hangs on two string segments, so if

B

descends with acceleration

a_B

, the string end at

A

moves with

a_A=2a_B

(constraint). For

A

T=2a_A

. For

B

(two segments pull up):

4g-2T=4a_B=2a_A

. Substituting

T=2a_A

40-4a_A=2a_A

, so

a_A=\dfrac{20}{3}\ \mathrm{m\,s^{-2}}

and

T=\dfrac{40}{3}\approx13.3\ \mathrm{N}

. Ignoring the factor 2 in the constraint gives a wrong tension.

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