First slide

Connected bodies

Question

A pendulum is hanging from the ceiling of a cage. When the cage is moving up with certain acceleration and when it is moving down with the same acceleration, the tensions in the strings are T₁ and T₂ respectively. When the cage moves horizontally with the same acceleration, the tension in the string is

Moderate

A

$\large \sqrt {2(T_1^2 + T_2^2)}$
B

$\large \sqrt {\frac{{T_1^2 + T_2^2}}{2}}$
C

$\large \sqrt {2(T_1^2 - T_2^2)}$
D

$\large \sqrt {T_1^2 + T_2^2}$

Solution

T₁ = m(g + a) ; T₂ = m(g – a)

$\fn_phv \large T_1^2 + T_2^2 =2 {m^2}({g^2} + {a^2})............(1)$
$\large T = m\sqrt {{a^2} + {g^2}} \Rightarrow {T^2} = {m^2}({g^2} + {a^2}).....(2)$
$\large T = \sqrt {\frac{{T_1^2 + T_2^2}}{2}}$

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