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 string are 7, and to respectively. When the cage moves horizontally with the
same acceleration, the tension in the string is,
​

Answer 1

Answer:

Final Answer :

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

2

T

1

2

+T

2

2

Steps:

1) Let the acceleration be 'a' in all cases.

We got,

When acceleration is downward,

$$\begin{lgathered}mg-T_2=ma \\ => T_2 =m(g-a) --(1)\end{lgathered}$$

2) When acceleration is upward ,

$$\begin{lgathered}T_1 -mg = ma \\ => T_1 = m(g+a) --(2)\end{lgathered}$$

3) When acceleration is horizontal,

$$\begin{lgathered}T \sin(\theta) = ma \\ T \cos(\theta) = mg \\ => T^2 = (mg)^2 + (ma)^2 \\ => T = m \sqrt{g^2 + a^2 }\end{lgathered}$$

4) Squaring eq. (1) and (2) :

$$\begin{lgathered}T_1^2 + T_2^2 = 2m^2( a^2 + g^2) \\ => T_1^2+ T_2^2 = 2T^2 \\ => T = \sqrt{\frac{T_1^2+T_2^2}{2}}\end{lgathered}$$

Hope , you got desired answer.