Question

A pendulum is hanging from the ceiling of a cage. When the cage is moving up with certain acceleration and when it is movng down with the same acceleration, the tension in the string are $T_1$ and $T_2$ repectively. When the cage moves horizontally with the same acceleration, the tension in the string is,

• A. $\sqrt{\frac{(T_1^2+T_2^2)}{2}}$
• B. $\sqrt{\frac{T_1^2{T}_2^2}{2}}$
• C. $\sqrt{2(T_1^2-T_2^2)}$
• D. $\sqrt{(T_1^2+T_2^2)}$

Answer 1

The correct option is A $\sqrt{\frac{(T_1^2+T_2^2)}{2}}$

Let the acceleration be, "a"

when the acceleration is downward,

$mg-T_2=ma\Rightarrow T_2=m(g-a)$..........(1)

when the acceleration is upward,

$T_1-mg=ma\Rightarrow T_1=m(g+a)$..........(1)

when the acceleration is horizontal,

$T\sin \theta =ma$

$T\cos \theta =mg$

$\Rightarrow T^2=(mg{)}^2+(ma{)}^2$

$\Rightarrow T=m\sqrt{g^2+a^2}$

squaring the eqns (1) and (2),

$T_1^2+T_2^2=2m^2(a^2+g^2)$

$T_1^2+T_2^2=2T^2$

$\therefore T=\sqrt{\frac{T_1^2+T_2^2}{2}}$