The centre of gravity of a loaded taxi is 1.5 m above the ground and the distance between its wheels is 2m. What is the maximum speed with which it can fo round an unbanked curve of radius 100 m without being turned upside down. What minimum value would the coefficient of friction is needed at this speed ?

A bend in a level road has radius of 100 m.Find the maximum speed with which a car turning this bend may have without skidding ,if the coefficient of friction between the tyres and road is 0.8.

A bend in a level road has a radius of 100 m.Find the maximum speed with which a car turning thi bend may have without skidding,if the co-efficient of friction between the tyres and the road is 0.2.

Tire ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m s^-1 can go without hitting the ceiling of the hall ?

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.

A stone of mass 0.25 kg tied to the end of a string is whirled round in a circle of radius 1.5 m with a speed of 40 rev.//min in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N ?

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?

A rheostat has 100 turns of a wire of radius 0.4 mm having resistivity 4.2 xx 10^-7Omega m. The diameter of each turn is 3 cm. What is the maximum value of resistance it can introduce?

A small retangular coil ABCD contains 140 turns of wire. The sides AB and BC of the coil are of length 4.5 and 2.8 cm respectively, as shown in the figure The coil is held between the poles of a large magnet so that the coil can rotate about an axis thorugh its centre. The magnet produces a uniform magnetic field of flux density B between its poles. When the current in the coil is 170 mA, the maximum torque produced in the coil is 2.1 xx 10^-3 N m . For the coil in the position shown in the figure. calculate the magnitude of the force on (i) side AB of the coil and (ii) side BC of the coil.

A steel cable with a radius of 1.5 cm supports a chairlift at a ski area. If the maximum stress is not to exceed 10^8 N m ^-2 , what is the maximum load the cable can support ?