A particle of mass 21g is attached to a string of length 70cm

A particle of mass 21g is attached to a string of length 70cm VI 04 MOTION ALONG A HORIZONTAL CIRCL€ AND MOTION OF VEHICLE ALONG CIRCULAR TRACKS 24. A particle of mass 21 g attached to a string of 70 cm length is whirled in a horizontal circle. If the of revolution is 2 s, find the tension in [Ans. 14509 dyne] the string. A ball of mass 0-1 kg is by a string 30 cm long. Keeping the string always taut, the ball describes a horizontal circle Of radius cm. Calculate the angular SB•ed Of the ball. (Ans. 6•14 rad./sl 26. A car of mass ISOOkg is moving with a speed Of rns-l on a circular path of radius 20 m on a level road What should the frictional force to avoid slipping Of car. Calculate the coefficient of [Ans. 1-172 N ; 0-81 27. What is angular velocity in rad s-l Of the hour, minute and second hand of a clock ? 3. What is the greatest speed at which a car having a track width of I S m can turn in a circular path of 24-5 m without overturning ? Assume that centre of gravity of the car is 049 m above the grcnand. Take g 98 mis2_ [Ans. 19•2 misl 29. of a massless svmng Of constant Im Nim natural length 0-5 m is fixed and the other end is connected to a particle of mass kg lying on a frictionless horizontal table. ne spring remains horizontal. If the mass is made to rotate at an uvular vel•xity of 2 rd's, find the elongation of smng. [Ans. I cml A of mass kg is whirled in a circle with a of 2 m s"' using m length of a string, which can withstand a tension of 15 N. Neglecting the force of gravity On the body. predict whether or tix string will break. Give reasons for ymar (Ans. The string will not break Centrifugal force is 4 N, which less than IS NI 31. The blades of an acroplanc pros*ller are 2 m long rate Of rpm, Calculate (i) the frequency Erriod of rotation (iii) the angular vehxity the unear vel'Rity of a B)int 0-5 m up of blade , S ; 3143 ; 47-15 m 32. maxunum SCRed at which a Car can turn a curve or 30 m radius on a level road if the of friction txtween the tyres and the [Ans. 11 m s-ll 4 33. A bend in a level road has a radius 01 the maximum speed which a car turning t: may have Without skidding. Coefficient of between tyres and road is 018. 28 AND BANKING OF R 34. An aeroplane travelling at a Of tilts at an angle of as it makes a Safe is the radius Of tlr curve ? [Ans. 3•41 35. A curve in a road forms an arc of radius "m the road is 196 m wide and outer edge i' higher than the inner edge, calculate the which it is banked. [Ans. 20 36. For traffic moving at 60 km/h, if the radius curve is (VI km. what is the correct angle banking of the road ? Given g 10 (Ans. 37. A cyclist goes round a circular track of 440 length in 20 seconds. Find the angle that his makes with the vertical. [Ans.3s• 38. A cyclist speeding at IS km/h on a level road a sharp circular turn Of radius 3 m without his speed. Will the cyclist slip while taku turn. if coefficient Of friction between the tyresQ road is 0-1 ? I Ans 39. An electric bulb suspended from the railway train by a flexible wire shifts angle of 190 48'. when the train goes round a curved path of 200 m radius. find Slk•ed of the train. [Ans. 26•56 A 200 kg car has to go over a turn Whose 750 m and the angle of slope is The of friction between the car wheels and 0-5. What should be the maximum speed Of car so that it may go Over the turn Wi slipping ? Take g = 9 •8 mjs2, (Ans. 672 41. A rnotor cyclist goes round a circular of diameter 320 m at 144 krn.m. How far fm vertical must he lean inwards to keep his balang Take g = 10m 42. The radius of curvature of a railway trackat• where the train is moving at a speed Of 72 kni is 625 m, Ille distance between the rails is Find the angle and the elevation Of the outa so that there may be no side pressure on the Take g 9-8 ms-2. [Ans. 3-74• ; MOTION A VERTICAL ciRC 43. ne railway bridge over a canal is in the an arc of a circle Of radius 20 m. What is minimum speed with which a car can crcss