A force of 100 N gives a mass m1, and a acceleration of 10 ms-2 and of

1.	A force of 100 N gives a mass m1, and a acceleration of 10 ms-2 and of 20 ms-2 to a mass m2. What acceleration must be given to it if both the masses are tied together?
Answer» Suppose, a = acceleration produced if m₁ and m₂ are tied together. F = 100 N. Let a₁ and a₂ be the acceleration produced in m₁ and m₂ respectively. ∴ a₁ = 10 ms^-2, a₂ = 20 ms^-2 (given) Again m₁ = \(\frac{F}{a_1}\) and m₂ = \(\frac{F}{a_2}\) or m₁ = \(\frac{100}{10}\) = 10 kg and m₂ = \(\frac{100}{20}\) = 5 kg ∴ m₁ + m₂ = 10 + 5 = 15 So, a = \(\frac{F}{m_1+m_2}\) = \(\frac{100}{15}\) = \(\frac{20}{3}\) = 6.67 ms^-2.

A force of 100 N gives a mass m1, and a acceleration of 10 ms-2 and of 20 ms-2 to a mass m2. What acceleration must be given to it if both the masses are tied together?

Answer»

Suppose, a = acceleration produced if m₁ and m₂ are tied together.

F = 100 N.

Let a₁ and a₂ be the acceleration produced in m₁ and m₂ respectively.

∴ a₁ = 10 ms^-2, a₂ = 20 ms^-2 (given)

Again m₁ = \(\frac{F}{a_1}\) and m₂ = \(\frac{F}{a_2}\)

or m₁ = \(\frac{100}{10}\) = 10 kg

and m₂ = \(\frac{100}{20}\) = 5 kg

∴ m₁ + m₂ = 10 + 5 = 15

So, a = \(\frac{F}{m_1+m_2}\) = \(\frac{100}{15}\) = \(\frac{20}{3}\)

= 6.67 ms^-2.