During the motion of a locomotive in a circular path of radus R, wind is blowing in the horizontal direction. The trace left by the smoke is shown in Fig. (topview.) Using the figure, determine the velocity `v_("wind")` of the wind if it is known to be constant, and if the velocity `v_(10c)` of the loco-motive is `36 km//h`.

A particle of mass m moves with constant speed v on a circular path of radius r as shown in figure. The average force on it during its motion from A to B is

A solid sphere is set into motion on a rough horizontal surface with a linear velocity v in the forward direction and an angular velocity v/R in the anticlockwise direction as shown in the figure. Find the linear speed of the sphere, when it stops rotating.

A particle P moves in a circular path of radius R, with centre at O at uniform speed v as shown in figure. At centre a bulb is glowing which forms a shadow S on ceiling at a height h above the ground. Find velocity of shadwo when particle P is at an angle 0 with the vertical:

A uniform circular disc of radius r placed on a rough horizontal plane has initial velocity v_(0) and angular omega_(0) as shown. The disc comes to rest after moving some distance in the direction of motion. Then

Two particle of mass m and 2m, connected by a massless rod, slide on the insider of a smooth circular ring of radius r, as shown in Fig. 3E.44 (a). If the assembly is released from rest when theta = 0 , determine (a) the velocity of the particle when the rod passes the horizontal position, (b) the maximum velocity v_("max") of the particles.

A particle of mass M attached to an inextensible strintg is moving in a vertical circle of radius R .about fixed point O . It is imparted a velocity u in horizontal directional at lowest position as shown in figure. Following information is being given (i) Velocity at a height h can be calculated by using formula v^(2)=u^(2)-2gh (ii) Particle will complete the circle if u ge sqrt(5gR) (iii) Particle will oscillates in lower half (0^(@)ltthetale90^(@)) if 0ltu lesqrt(2gR) (iv) The magnitude of tension at a height 'h' is calculated by using formula T=M/R[u^(2)+[gR-3gh]] If M = 2kg, R = 2m and u = 10 m//s . Then velocity of particle when theta = 60^(@) is

A particle of mass M attached to an inextensible strintg is moving in a vertical circle of radius R .about fixed point O . It is imparted a velocity u in horizontal directional at lowest position as shown in figure. Following information is being given (i) Velocity at a height h can be calculated by using formula v^(2)=u^(2)-2gh (ii) Particle will complete the circle if u ge sqrt(5gR) (iii) Particle will oscillates in lower half (0^(@)ltthetale90^(@)) if 0ltu lesqrt(2gR) (iv) The magnitude of tension at a height 'h' is calculated by using formula T=M/R[u^(2)+[gR-3gh]] If R = 2m, M = 2 kg and u = 12 m//s . Then value of tension at lowest position is

A particle of mass M attached to an inextensible strintg is moving in a vertical circle of radius R .about fixed point O . It is imparted a velocity u in horizontal directional at lowest position as shown in figure. Following information is being given (i) Velocity at a height h can be calculated by using formula v^(2)=u^(2)-2gh (ii) Particle will complete the circle if u ge sqrt(5gR) (iii) Particle will oscillates in lower half (0^(@)ltthetale90^(@)) if 0ltu lesqrt(2gR) (iv) The magnitude of tension at a height 'h' is calculated by using formula T=M/R[u^(2)+[gR-3gh]] Tension at highest point of its trajectory in above question will be

Rain water is falling vertically downward with velocity v . When velocity of wind is u in horizontal direction, water is collected at the rate of R m^(3)//s . When velocity of wind becomes 2u in horizontal direction. The rate of collection of water in vessel is