A trolley of mass 300 kg carrying sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, sand starts leaking out of a hole on the floor of the trolley at the rate of 0.05kg s^(-1) . What is the speed of the trolley after the entire sand bag is empty?

A trolley of mass 30 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track . After a while , sand starts leaking out of hole on the floor of the trolley of the rate of 0.05 " kg s"^(-1) .What is the speeed of the trolley after the entire sand bad is empty ?

A trolley of mass 200 kg moves with a uniform speed of 36 km/h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of 4 ms^(-1) relative to the trolley in a direction opposite to the its motion, and jumps out of the trolley. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?

One end of a string of length I is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is

One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is : (i) T, (ii) T - (mv^2)/(l) , (iii) T + (mv^2)/(l) , (iv) 0 T is the tension in the string. [Choose the correct alternative].

Figure shows a metal rod PQ resting on the smooth rails AB and positioned between the poles of a permanent magnet. The rails, the rod, and the magnetic field are in three mutual perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod =15 cm, B =0.50 T, resistance of the closed loop containing the rod 9.0 m Omega . Assume the field to be uniform. (a) Suppose K is open and the rod is moved with a speed of 12 "cm s"^(-1) in the direction shown. Give the polarity and magnitude of the induced emf. (b) Is there an excess charge built up at the ends of the rods when K is open ? What if K is closed ? (c) With K open and the rod moving uniformly, there is no net force on the electrons in the rod PQ even though they do experience magnetic force due to the motion of the rod. Explain. (d) What is the retarding force on the rod when K is closed ? How much power is required (by an external agent) to keep the rod moving at the same speed (= 12 cm s^(-1) ) when K is closed ? How much power is required when K is open? (f)How much power is dissipated as heat in the closed circuit ? What is the source of this power ? (g) What is the induced emf in the moving rod if the magnetic field is parallel to the rails instead of being perpendicular ?

A trolley was moving horizontally on a smooth ground with velocity v with respect to the earth. Suddenly a man starts running from rear end of the trolley with a velocity (3//2)v with respect to the trolley. After reaching the other end, the man turns back and continues running with a velocity (3//2)v with respect to trolley in opposite direction. If the length of the trolley is L, find the displacement of the man with respect to earth when he reaches the starting point on the trolley. Mass of the trolley is equal to the mass of the man.

On a long horizontally moving belt (From figure) a child runs to and fro with a speed 9 kmh^(-1) (with respect to the belt) between his father and mother located 50 m apart on the moving belt. The belt moves with a speed of 4 kmh-l. For an observer on a stationary platform outside, what is the (a) Speed of the child running in the direction of motion of the belt ? (b) Speed of the child running opposite to the direction of motion of the belt ? (c) Time taken by the child in (a) and (b) ? Which of the answers alter if motion is viewed by one of the parents ?

On a long horizontally moving belt, a child runs to an fro with a speed 9 kmh^(-1) ( with respect to the belt) between his father and mother located 50m a part on the moving belt. The belt moves with a speed of 4 kmh^(-1) . For an observer on a stationery platform outside, what is the (i) speed of the child running in the direction of motion of the belt, (ii) speed of the child running opposited to the direction of motion of the belt , and (iii) time taken by child in (i) and (ii) ? which of the answers alter if motion is viewed by one of the parents?

A thin homogeneous rod of mass m and length l is free to rotate in vertical plane about a horizontal axle pivoted at one end of the rod. A small ballof mass m and charge q is attached to the opposite end of this rod. The whole system is positioned in a horizontal electric field of magnitude E=(mg)/(2q) . The rod is released from, shown position from rest. What is the speed of ball when rod becomes vertical?