प्रश्न 20. एक कण सरल आवर्त गति से एक सरल रेखा पर गतिमान है। जब कण की केन्द्र से दूरी \( x_{1} \) तथा \( x_{2} \) है तथा इसक वेग कमशः \( \nu_{1} \) तथा \( v_{2} \) है। सिद्ध कीजिये कि आवर्त काल होगा

Question ix. An ideal gas is enclosed in a cylinder which has a movable piston. The gas is heated, resulting in an increase in temperature of the gas, and work is done by the gas on the piston so that the presure remains constant. a) Is the work done by the gas negative, positive or zero? b) From a microscopic view, how is the internal energy of the gas molecules affected? c) Is the heat less than, greater than or equal to the work? Explain you answer.

A boat is supposed to travel with a velocity vector of \( \langle 40,30\rangle \), but the current has a velocity vector of \( \langle 0,-5\rangle \). What is the boat's actual velocity vector? \( \langle 45,30\rangle \) \( \langle 40,25\rangle \) \( \langle 40,35\rangle \)

14. A train moving at an average speed of \( 72 \mathrm{~km} / \mathrm{h} \) takes 15 seconds to completely cross a bridge that is 80 metres long (a) Express \( 72 \mathrm{~km} / \mathrm{h} \) in metres per second (b) Find the length of the train in metres ( 2 mk )

A 1 km long goods train is running at a speed of 45 \( \mathrm{~km} / \mathrm{h} \). The time taken by this goods train to pass through a 2 km long tunnel is: \( \begin{array}{ll}\text { (A) } 1 \text { minute } & \text { (B) } 2 \text { minutes } \\ \text { (C) } 3 \text { minutes } & \text { (D) } 4 \text { minutes }\end{array} \)

Problem (1) uniform bar \( A B \) of mass 40 kg and 8 m length is fixed in a vertical plane by two strings \( A D \) Id \( B H \), and a body of mass 60 kg is humg at a point \( C \) on \( A B \) so the bar became in an quilibrium state horizontally, and \( m(\angle D A B)=120^{\circ}, m(<H B A)=150^{\circ} \). find the magnitude fine tension in each of the strings and the length \( \overline{A C} \). Answer.