Problem Statement: A small ball is suspended by a string from the ceiling of a car. As the car accelerates at a rate of 'a', the string makes an angle theta with equilibrium in vertical. Find the tension in the string.

Explanation:
To solve the problem, we need to consider the forces acting on the ball. The forces acting on the ball are:

1. Force due to tension in the string, T
2. Force due to the weight of the ball, mg
3. Force due to the acceleration of the car, ma

We can resolve these forces into components along the vertical and horizontal directions. The vertical component of the tension in the string balances the weight of the ball, and the horizontal component of the tension in the string balances the force due to the acceleration of the car.

Using trigonometry, we can relate the tension in the string to the angle theta:

cos(theta) = F_horizontal/T
sin(theta) = F_vertical/T

where F_horizontal and F_vertical are the horizontal and vertical components of the tension in the string, respectively.

We can solve for F_horizontal and F_vertical by using the following equations:

F_horizontal = T * cos(theta)
F_vertical = T * sin(theta) - mg

Since the ball is in equilibrium, the net force acting on it must be zero. Therefore,

F_horizontal = ma

Substituting F_horizontal in terms of T and theta, we get:

T * cos(theta) = ma

Solving for T, we get:

T = ma / cos(theta)

Substituting F_vertical in terms of T and theta, we get:

T * sin(theta) - mg = 0

Solving for T, we get:

T = mg / sin(theta)

We can use either of these equations to find the tension in the string.

Conclusion:
The tension in the string is given by:

T = ma / cos(theta) = mg / sin(theta)

where m is the mass of the ball, g is the acceleration due to gravity, a is the acceleration of the car, and theta is the angle made by the string with the vertical.

What is the answrr?? m√g(squared)+ a(squard) ?