ANURAG TYAGI CLASSES, ATC HOUSE ,10 C-82, VASUNDHRA, GHAZIABAD CALL US @ 09818777622 BRANCH: 6/ 93, SATYAM APPARTMENT, RAJENDR NAGAR,SAHIBABAD.

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Kinematics BY ANURAG TYAGI SIR ( ATS)

Q1. a particle originally at rest at the highest point of a smooth vertical circle of radius R, is slightly displacement .find the distance below the highest point where the particle will leave the circle?{h =R/3} Q2. The sum of the magnitudes of two forces acting at a point is 18N and the magnitude, what is the magnitude of forces? {13N} Q3.if a body travels half of its path in the last second of its fall from rest; fund the time and height of its fall? {3.1414s} Q4.an object A is kept fixed at the point x = 3m and y=1.25m on a moving along the +x direction with an acceleration 1.5 m/s. At the same instant a stone hitting the object during its downward motion at an angle pf 45º to the horizontal .all the motions are in X-Y plane .find u and time after which stone hits the object. Take g = 10m/s² Q5.three particles a, b and c are situated at the vertices of an equilateral triangle abc of side d at t = 0. Each of the particles moves with constant speed v. A always has its velocity along BC and C along CA. At what time will the particles meet each other? {t= 2d/3v} Q6.a man standing on road has to hold his umbrella at 30º with the vertical to keep the rain away he throws the umbrella and starts running at 10 km/h. he finds that raindrops with respect to [a]the road, [b] the moving man.{10√3 km/h} Q7.a man can swim at speed of 3 km/h in still water. He wants to cross a 500 m wide river flowing at 2 km/h. he keeps himself always at an angle of 120º with the river flow while swimming.(a)find the time he takes to cross river . (b) At what point on the opposite bank will he arrive?{1/3√3h, 1/6√3 km} Q8. a staircase contains three steps each 10cm high and 20 cm wide what should be the minimum horizontal velocity of a ball rolling off the uppermost plane so as to hit directly the lowest plane ? {2m/s} Q9. a person is standing on a truck moving with a constant velocity of 14.7 m/s on a horizontal road .The man throws a ball in such a way that it returns to the truck after the truck has moved 58.8 m .find speed and the angle of projections (a) as seen from the truck, (b) as seen from the road {(a) 19.6 m/s upward (b) 24.6 m/s at 53º with horizontal} Q10. An airplane has to go from a point A to another point B, 500 km away due 30º east of north. a wind is blowing due north at a speed of 20 m/s (a) find the direction in which the pilot should head the plane to reach the time taken by the plane to go from A to B { (a) sinֿ¹(1/15) east of the line AB,(b) 50 min} objectives

Q1. a particle is projected at 60º to the horizontal with a kinetic energy K. the kinetic energy at the highest point

(a) /2 (c) zero

(b) (d) K/4

Q2. a small block slides without friction down an inclined plane starting from rest . let Sn be the distance traveled from time t = (n-1) to t = n then Sn /Sn+1 is

(a) n-1/2n (b) n+1/2n-1 (c) n-1/2n+1 (d) n/2n+1

Q3. Which of the following statements is false for a particle moving in a circle with a constant angular speed?

(a) he velocity vector is tangent to the circle (b) he acceleration vector is tangent to the circle (c) he acceleration vector points to the centre of the circle (d) he velocity and acceleration vectors are perpendicular to each other

Q4.A car is moving in a circular horizontal track of radius 10.0 m with a constant speed of 10.0m/s.A plumb bomb is suspended from the roof of the car by a light rigid rod of length1.00 m. The angle made by the rod with the track is (g= 10 m/s²) (a) zero (b) 30º (c) 45º (d) 60º Q5. The distance traveled by an object along the axes are given by x=2t², y = t² - 4, z = 3 t - 5. The initial velocity of the particle is

(a)10 units (b)12 units (c)5 units (d)2 units

Q6. A boy playing o the roof of 10m high building

throws a ball with a speed of 10/s at an angle of 30º the horizontal. How far from the throwing point will the ball be at the height of 10m from the ground ?

(a) 5.20 m (b) 4.33 m

ANURAG TYAGI CLASSES, ATC HOUSE ,10 C-82, VASUNDHRA, GHAZIABAD CALL US @ 09818777622 BRANCH: 6/ 93, SATYAM APPARTMENT, RAJENDR NAGAR,SAHIBABAD.

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(c) 2.60 m (d) 8.66 m Q7 A parachutist after bailing out falls 50 m without

friction. When parachute opens. it decelerates at 2msֿ².He reaches the ground with a speed of 3msֿ¹. At what height did he bail out?

(a) 111m (b)293m (c)182m (d) 91m

Q8. A car runs at a circular track at a constant speed or radius 100 m, taking 62.8 seconds for every circular lap. The average velocity and average speed for each circular lap respectively is (a) 10m/s (b) 0,0 (c) 0.10m/s (d) 10m/s,10m/s

Q9. A particle is moving on a straight line path constant acceleration directed along the direction of instantaneous velocity. Which of the statement are false about the motion of particle?

(a) the average velocity is less then the average speed (b) the average velocity is equal to the instantaneous

speed (c) the distance covered is equal to the magnitude of

displacement (d) the particle may reverse the direction of motion 156

Q10.Select the correct statement for a particle going on a straight line

(a) if the position and velocity are in opposite direction then, The particle is moving towards the origin.

(b) If the acceleration and velocity are in opposite direction, the particle is slowing down

(c) If the velocity is zero for a time interval, the acceleration is zero at any moment within that time interval

(d) If the velocity is zero at any instant , then the acceleration must also be zero at that instant 160

Rotational and Mechanics Objectives: Q1.A thin circular ring of mass M and radius r is

rotating about its axis with a constant angular velocity ω. Two objects each of mass m, are attached gently to the opposite ends of a diameter of the ring. The wheel now rotates with an angular velocity:

(a) ω M / (M+m) (b) ω M / (M+2m)

(c) ω( M -2m) / (M+2m) (d) ω (M+2m)/M Q2. Two point masses of 0.3 kg and 0.7 kg are fixed

at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum, is located at a distance of;

(a) 0.42 m from mass of 0.3 kg (b) 0.70 m from mass of 0.7 kg (c) 0.98 m from mass of 0.3 kg (d) 0.98 m from mass of 0.7 kg

Q3. A mass m is moving with a constant velocity

along a line parallel to the x- axis, away from the origin . Its angular momentum with respect to the origin:

(a) is zero (b) remains constant (c) goes on increasing (d) goes on decreasing

Q4. A cylinder rolls up an inclined plane , reaches some height and then rolls down ( without slipping throughout these motions ). The directions of the frictional force acting on the cylinder are :

(a) up the inclined while ascending and down the inclined while descending

(b) up the inclined while ascending as well as descending

(c) down the inclined while ascending and up the inclined while descending

(d) down the inclined while ascending as well as descending

Q5. A child is standing with folded hands at the center of a platform rotating about its centre axis . º√The kinetic energy of the system is K. The child now starches his arms so that the moment of inertia of the system doubles The kinetic energy of the system now is (a) 2K (b) K/2 (c) K/4 (d) 4K

Q6. A particle moves in a circular path with decreasing speed Choose the correct statement;

(a) angular momentum remains constant (b) Acceleration is towards the centre (c) Particle moves in a spiral path with decreasing

radius

ANURAG TYAGI CLASSES, ATC HOUSE ,10 C-82, VASUNDHRA, GHAZIABAD CALL US @ 09818777622 BRANCH: 6/ 93, SATYAM APPARTMENT, RAJENDR NAGAR,SAHIBABAD.

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(d) The direction of angular momentum remains constant.

Q7. A particle undergoes uniform circular motion. About which point on the plane of the circle , will the angular momentum of the particle remains conserved? (a) Center of circle (b) On the circumference of the circle (c) Inside the circle (d) Out side the circle

Q8. A smooth sphere A is moving on a frictionless horizontal plane with angular velocity ω and centre Of mass velocity v. it collides elastically and head on with an identifical sphere B at rest . neglect Friction everywhere . after the collision their angular speeds as ώ- and ώ-- respectively (a) ώ- < ώ-- (b) ώ- = ώ-- (c) ώ- = ω (d) ώ-- = ω Q9. A cylinder rolls up an inclined plane ,reaches some height and then rolls down (without slipping Throughout these motions ). The directions of the frictional force action on the cylinder are :

(a) up the incline while ascending and down the incline while descending

(b) up the incline while ascending as well as descending

(c) Down the incline while ascending and up the incline while descending

(d) Down the incline while ascending as well as descending

Q10.A practicle undergoes uniform circular motion . about which point on the plane of the circle ,will the angular momentum of the particle remain conserved ? (a) Centre of circle (b) On the circumference of the circle (c) Inside the circle (d) Outside the circle