When an object is whirled in a horizontal plane, the tension in the string provides the centripetal force required to keep the object in circular motion. The centripetal force is given by the formula:
F = m ⋅ ω² ⋅ r
where m is the mass of the object, ω is the angular velocity, and r is the radius of the circular path.
Initially, the tension T in the string is equal to the centripetal force:
T = m ⋅ ω² ⋅ r
When the speed becomes 2ω, the new tension T' in the string is:
T' = m ⋅ (2ω)² ⋅ r
Simplifying, we get:
T' = m ⋅ 4ω² ⋅ r
Therefore, the new tension T' is four times the initial tension T:
T' = 4T
Step-by-Step Solution:
Step 1: Identify the initial tension in the string
T = m ⋅ ω² ⋅ r
Step 2: Determine the new angular velocity:
2ω
Step 3: Calculate the new tension in the string using the new angular velocity:
T' = m ⋅ (2ω)² ⋅ r
Step 4: Simplify the expression to find the new tension:
T' = 4T
Final Answer:
The tension in the string becomes 4T.
A simple pendulum is made of a metal wire of length \( L \), area of cross-section \( A \), material of Young's modulus \( Y \), and a bob of mass \( m \). This pendulum is hung in a bus moving with a uniform speed \( V \) on a horizontal circular road of radius \( R \). The elongation in the wire is:
The velocities of air above and below the surfaces of a flying aeroplane wing are 50 m/s and 40 m/s respectively. If the area of the wing is 10 m² and the mass of the aeroplane is 500 kg, then as time passes by (density of air = 1.3 kg/m³), the aeroplane will:
List I | List II | ||
A | Down’s syndrome | I | 11th chormosome |
B | α-Thalassemia | II | ‘X’ chromosome |
C | β-Thalassemia | III | 21st chromosome |
D | Klinefelter’s syndrome | IV | 16th chromosome |
The velocity (v) - time (t) plot of the motion of a body is shown below :
The acceleration (a) - time(t) graph that best suits this motion is :