Introduction:
When a mass is suspended from a spring balance, the balance measures the weight of the mass, which is equivalent to the force of gravity acting on it. However, when the mass is pulled aside by a horizontal string, its weight is no longer acting vertically downward. In this scenario, the reading on the spring balance will change due to the change in the direction of the weight vector.

Explanation:
To determine the new reading of the spring balance, we need to consider the components of the weight vector. The weight vector can be divided into two components: one along the vertical direction and the other along the horizontal direction.

Vertical Component:
The vertical component of the weight vector is equal to the weight of the mass, which can be calculated using the formula:
Weight = mass * gravitational acceleration
In this case, the mass is given as 10 kg, and the gravitational acceleration is approximately 9.8 m/s^2. Therefore, the vertical component of the weight is:
Vertical Component = 10 kg * 9.8 m/s^2 = 98 N

Horizontal Component:
The horizontal component of the weight vector can be determined by multiplying the vertical component by the tangent of the angle made by the string with the vertical. In this case, the angle is given as 60 degrees. Therefore, the horizontal component of the weight is:
Horizontal Component = Vertical Component * tan(60 degrees)
Horizontal Component = 98 N * tan(60 degrees) ≈ 169.65 N

New Reading of the Spring Balance:
The new reading of the spring balance will be the vector sum of the vertical and horizontal components of the weight. Since the spring balance measures the magnitude of the force, we need to find the resultant force using the Pythagorean theorem:
Resultant Force = sqrt(Vertical Component^2 + Horizontal Component^2)
Resultant Force = sqrt(98 N^2 + 169.65 N^2) ≈ 196.78 N

Therefore, the new reading of the spring balance when the mass is pulled aside by a horizontal string and makes an angle of 60 degrees with the vertical is approximately 196.78 N. This reading takes into account both the vertical and horizontal components of the weight vector.

50 kg