two charged particles having charge 4.0X 10-6C and mass 24×10-3kg each are joined by an insulating string of length 1 m and the system is kept on a smooth horizontal table.find the tension in the string
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Two charge particles having charge q = 4 × 10⁻⁶C and mass , m = 24 × 10⁻³ Kg as are joined by an insulting string of length 1 m as shown in figure .
Here we arranged free body diagram of right particles .
after resolution of tension in string we get, upward force due to tension = Tcosθ and Rightward force = Tsinθ . Because both the given charge particles are same nature so, both particles repel each other.
Force act between them , F = Kq²/x² , here x = 2Lsinθ = 2 ×1 × sinθ m
so, F = Kq²/4sin²θ
= 9 × 10⁹ × (4 × 10⁻⁶)²/4sin²θ
= 36 × 10⁻³/sin²θ N ,
and weight = mg = 0.024 × 10 = 0.24 N
Here is clear that ,
downward force = upward force
mg = Tcosθ ------(1)
leftward force = rightward force
F = Tsinθ ------(2)
squaring and adding of both equations
(mg)² + F² = T²
T = √{m²g² + F²}
T = √{(0.24)² + 0.036cosec²θ} , here for finding θ more information required .
Here we arranged free body diagram of right particles .
after resolution of tension in string we get, upward force due to tension = Tcosθ and Rightward force = Tsinθ . Because both the given charge particles are same nature so, both particles repel each other.
Force act between them , F = Kq²/x² , here x = 2Lsinθ = 2 ×1 × sinθ m
so, F = Kq²/4sin²θ
= 9 × 10⁹ × (4 × 10⁻⁶)²/4sin²θ
= 36 × 10⁻³/sin²θ N ,
and weight = mg = 0.024 × 10 = 0.24 N
Here is clear that ,
downward force = upward force
mg = Tcosθ ------(1)
leftward force = rightward force
F = Tsinθ ------(2)
squaring and adding of both equations
(mg)² + F² = T²
T = √{m²g² + F²}
T = √{(0.24)² + 0.036cosec²θ} , here for finding θ more information required .
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