An aeroplane requires for take off a speed of `80km h^(-1)`, the run on the ground being 100m. The mass of the plane is 10000 kg and the coefficient of friction between the plane and the ground is 0.2. Assume that the plane accelerates uniformly during the take off. What is minimum force required by the engine of the plane for take off ?

A cyclist speeding at 18 km h^-1 on a level road makes a sharp circular turn of radius 3 m without reducing the speed. The coefficient of static friction between the tyres and the road is 0.1 will the cyclist slip while taking the turn?

The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in Fig. 5.22. The coeffcient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with 2 m s^-2 . At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).

Figure 5.18 shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with 1 m s^-2 . What is the net force on the man? If the coefficient of static friction between the man’s shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt ? (Mass of the man = 65 kg.)

The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown. The coefficient of friction between the box and the surface below its is 0.15. On a straight road, the truck starts from rest and accelerates with 2 ms^-2 . At what distance from the starting point does the box fall off the truck ?/ (Ignore the size of the box).

A boy whirls a stone in a horizontal circle 2 m above the ground by mean of a string 1.25 m long .The string breaks nd the stone flies off horizontally,striking the ground 10 m away.What is the magnitude of the centripetal acceleration during circular motion ?Take g= 10 ms^-2 .

A train runs along an unbanked circular track of radius 30 m at a speed of 54 km//h . The mass of the train is 10^6 kg . What provides the centripetal force required for this purpose — Hie engine or the rails ? What is the angle of banking required to prevent wearing out of the rail ?

A small sphere rolls down without slipping from the top of a track in a vertical plane. The track has an elevated section and a horizontal part is 1.0 m above the ground level and the top of the track is 2.4 m above the ground. Find the distance on the ground with respect to the point B (which is vertically ) below the end of the track as shown in figure. Where the sphere lands. During its flight as a projectile does the sphere continue to rotate about its centre of mass? Explain.

When a car moving with 36 km h^(-1) reaches an upward inclined road of angle 30^@ ,its engine is switched off.If the co-efficient of friction is 0.1,how much distance will the car move before coming to rest ?(Take = 10 m s^(-2) ).

A plane is in level flight at constant speed and each of its two wings has an area of 25 m^2 . If the speed of the air is 180 km//h over the lower wing and 234 km//h over the upper wing surface, determine the plane’s mass. (Take air density to be 1 kg m^-3 )

On complete combustion a litre of petrol gives off heat equivalent to 3 xx 10^7 J . In a test drive a car weighing 1200 kg, including the mass of driver, runs 15 km per litre while moving with a uniform speed on a straight track. Assuming tha friction offered by the road surface and air to be uniform, calcuate the force of friciton acting on the car during the test drive, if the efficiency of the car engine were 0.5.