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mc\(\Delta\theta\) = m\(\lambda\)\(_f\) 2 x 400 (100 - 0) = m(3.3 x 10\(^{5}\)) m = \(\frac{2 \times 400 \times 100}{3.3 \times 10^{5}} = \frac{8}{33}\)kg

Given m = 10\(^{-2}\) w = 100rads\(^{-1}\) F = mw\(^{2}\)r r = 0.2m F = ? = 10\(^{-2}\) x (100)\(^{2}\) x 0.2 = 20N

Givn m = 0.1kg u = 10ms\(^{-1}\) h = 10m g = 10ms\(^{-2}\) At h\(_{max}\); v = 0 Using \(\not v\) = \(\not u\) = \(\not gt\) \(\not 0\) = \(\not w\) - \(\not 10t\) v\(^{2}\) = u\(^{2}\) - 2gh 0\(^{2}\) = 10\(^{2}\) - 2 x 10h 20h = 100 h = 5m Total height = 10 + 5 = 15m Total energy = mghr = 0.1 x 10 x1 5 = 15J

\(\frac{\bigtriangleup s}{\bigtriangleup t}\) = uniform velocity

Given \(\frac{m_{1}}{m_{2}} = \frac{3}{1}\) \(\Rightarrow\) \(m_1\) = 3\(m_2\) \(\frac{a_{1}}{a_{2}} = \frac{2}{9}\) = \(a_1\) = \(\frac{2a_{2}}{9}\) \(\frac{F_{1}}{F_{2}}\) = ? Since F = ma \(\Rightarrow\) \(\frac{F_{1}}{F_{2}} = \frac{m_{1}a_{1}}{m_{2}a_{2}}\) = \(\frac{(3 \not m_{2})(2 \not a_{2})}{\not m_{2} a_{2} \not a_{3}}\) \(\frac{F_{1}}{F_{2}} = \frac{2}{3}\) \(\Rightarrow\) 2:3

R.D = \(\frac{\text {weigh in air - weigh in liquid X}}{\text {weigh in air - weigh in water}}\) = \(\frac{10 - 7}{10 - 6} = \frac{3}{4}\)

Using; \(m_1\) \(u_1\) + \(m_2\) \(u_2\) = (\(m_1\) + \(m_2\))v \(m_1\) = 0.5kg, \(u_1\) = 10ms\(^{1}\), \(m_2\) = 0.5kg, \(u_1\) = 0 \(\therefore\) (0.5kg x 10) + (0.5 x 0) = (0.5 + 0.5)v v = 5ms\(^{1}\)

Given \(m_1\) = 0.05kg, \(u_1\) = 200ms\(^{-1}\), \(m_2\) = 0.95kg K.E = \(\frac{1}{2}\)\(m_r\)v\(^{2}\) \(m_1\)\(u_1\) = v(\(m_1\) + \(m_2\)) [law of conversation of momentum] v = \(\frac{0.05 \times 200}{0.05 + 95}\) = 10ms\(^{-1}\) K.E = \(\frac{1}{2}\)(1)10\(^{2}\) = 50J

In simple harmonic motion, the acceleration of the particle is directed towards its mean position and directly proportional to its displacement.

Frictional force opposes motion

Surface tension decreases by: * Increasing liquid's temperature * Adding soap to the liquid

Young's modulus \(\frac{stress}{strain}\) Strain = \(\frac{e}{l} = \frac{0.05}{10} = \frac{10^{7}}{0.005}\) 2 x 10\(^{9}\)Nm\(^{-2}\)

, displacement, velocity, and acceleration, linear momentum, force are vector quantities, while speed (the magnitude of velocity), time, and mass are scalars. To qualify as a vector, a quantity having magnitude and direction must also obey certain rules of combination.

Pressure varies inversely as A i.e P \(\propto\) \(\frac{1}{A}\)

The collision between the gases is perfectly elastic