Uniform and Non Uniform

Q. A block A of mass m1 rests on a horizontal table a light string connected to it passes over frictionless pulley at the edge of table and from its othe end another block B of mass m2 is suspended the coefficient of kinetic friction between the block and table is μ k when the block A is sliding on the table the tension in the string is

Q.

Consider a car moving along a straight horizontal road with a speed of 72 km/h. If the coefficient of kinetic friction between the tyres and the road is 0.5, the shortest distance in which the car can be stopped is $[g=10m/s^{-2}]$

1. 40 m

2. 72 m

3. 20 m

4. 30 m

Q.

A car is moving along a straight horizontal road with a speed $v_0$. If the coefficient of friction between the tyres and the road is $\mu$, the shortest distance in which the car can be stopped is

1. 

2. 

3. 

4. 

Q. A uniform thin cylindrical disk of mass M and radius Ris attached to two identical massless springs of springconstant k which are fixed to the wall as shown in thefigure. The springs are attached to the axle of the disksymmetrically on either side at a distance d from itscentre. The axle is massless and both the springs andthe axle are in a horizontal plane. The unstretched lengthof each spring is L. The disk is initially at its equilibriunmposition with its centre of mass (CM) at a distancefrom the wall. The disk rolls without slipping with velocityVo Voi . The coefficient of friction is u. \lbrack IT-JEE 2008\rbrack

Q. { A stone of mass }1 kg is tied with a string and it }}{ is whirled in a vertical circle of radius }1m . If }}{ tension at the highest point is }14N , then velocity }} at lowest point will be }{ (1) }3m/s}{ (3) }6m/s

Q. a ball is projected from origin with speed 20m/s at an angle 30 with x axis the x coordinate of the ball at the instant when the velocity of the ball becomes perpendicular to the velocity of projection will be

Q.

A car of mass ‘m’ is driven with acceleration ‘a’ along a straight level road against a constant external resistive force ‘R’. When the velocity of the car is ‘v’, the rate at which the engine of the car is doing work will be

1. Rv

2. mav

3. (R+ma)v

4. (ma-R)v

Q. { 12. }80 railway wagons all of same mass }5×10^3kg} are pulled by an engine with a force of }{4×10^5N . The tension in the coupling between }}{30 th and }31st wagon from the engine is :-

Q. An unbanked curve has a radius of 60 m. Coefficient of friction between the tyre of truck and road is 0.75 The distance between two front wheel of truck is 2 m. If the truck exceeds the speed ofsafe limit, then their inner wheel leaves the the ground first why

Q. A car moves linearly with uniform retardation. If the car covers 40 m in the last 2 seconds of its motion , what is the velocity of the car at the beginning of the last second ?

Q.

A particle is projected from the ground at t = 0 so that on its way it just clears two vertical walls of equal height on the ground. If the particle passes just grazing the top of the walls at time $t=t_1$ and $t=t_2$ then calculate the height of the walls.

1. 

2. 

3. 

4. 

Q.

The velocity of a particle varies with time at $V\left(t\right)=e^{-2\pi t}$. Find the diaplacement of the particle till $t=(\frac{1}{2\pi })$ sec.

1. 

2. 

3. e

4. 

Q. what is the practical meaning of having time period infinity by a body doing SHM during free fall

Q. Figures (i) and (ii) below show the displacement-time graphs of two particles moving along the x-axis. We can say that

1. Both the particles are having a uniformly retarded motion
2. Both the particles are having a uniformly accelerated motion
3. Particle (i) is having a uniformly accelerated motion while particle (ii) is having a uniformly retarded motion
   
4. Particle (i) is having a uniformly retarded motion while particle (ii) is having a uniformly accelerated motion
   

Q. The ratio of the acceleration for a solid sphere (mass m and radius R) rolling down an incline of angle θ without slipping and slipping down the incline without rolling is

Q. 50. a car starting from the rest accelerates uniformly at the rate of 1m/s2 and attains a speed� of 10m/s .then it continues� to move� with the same speed for same time .then deaccelerates uniformly� at the rate of 2m/s2and the finally comes to rest, if the total time taken is 25s.the tital distance travelled is

Q. The velocity of a particle as a function of its position x is expressed as v=(c1+c2x) where c1 and c2 are positive constants. The acceleration of particle is?

Q.

The acceleration at any instant is the slope of the tangent of the _______curve at that instant:

1. x-v

2. v-t

3. a-t

4. x-t

Q. a solid flywheel of 20 kg mass and 120 mm radius revolves at 600 RPM with what force must a brake lining be pressed against it for the flywheel to stop in 3 second if the coefficient of friction is 0.1

Q.

A car of mass m is driven with acceleration a along a straight level road against a constant external resistive force R. When the velocity of the car is V, the rate at which the engine of the car is doing work will be

1. RV

2. maV

3. 

4. 

Q. A gun with a mount is placed on a smooth horizontal surface. The mount is attached with a light spring of spring constant k. The mass of bullet is m and mass of gun and mount is M. If a bullet is fired with velocity v horizontally, then maximum compression of spring is [given M>>m]

Q. find the maximum speed with which a car can turn on a bend without skidding, if radius of bend is 20 m and coefficient of friction between the road and the tyres is 0.4

Q. 143.In the given diagram find the acceleration of the block with respect to the disk

Q.

Diagram shows the direction of the total acceleration and velocity of a particle moving clockwise in a circle of radius 5/√3 m at an instant of time. Tangential acceleration at this instant is 5 m/s². Which of the following statements is not correct?

1. The centripetal acceleration is

2. Uniform circular motion

3. The net acceleration is 10

4. The particle is slowing down

Q. 52. The minimum stopping distance of a car moving with no velocity v is x. If the car is moving with velocity 2v then the minimum stopping distance will be

Q. One end of an ideal spring having spring constant100 N/m is converted to a block of mass 4 kg. Theother end of the spring is fixed. The block lies ona smooth horizontal surface. If the block is pushedso that the spring is compressed by 10 cm andreleased from rest: The speed of the block whenspring regains its original length is

Q. .A police van moving with a speed of V_o km/h on theroad fires a bullet at a thiefs car speeding away inthe same direction with a speed 6V_o, km/h. If the muzzle speed of the bullet is 20V_o km/h, then the speed of the bullet by which it hits the thiefs car is(1)15V_o(2)V_o(3)2V_o(4)13V_{

Q. Given: $v=0.6-0.3t$ (in SI units). The acceleration is

1. $-0.3{\text{ms}}^{-2}$
2. $0.6{\text{ms}}^{-2}$
3. $2.4{\text{ms}}^{-2}$
4. $3.6{\text{ms}}^{-2}$

Q. 2000 small balls, each weighing 1 g, strike onesquare cm of area per second with a velocity of100 m/s normal to the surface and rebounds withthe same velocity. The pressure on the surface is

Q. A particle is moving in a straight path with an acceleration $a=bn$, where $b$ is a positive constant $(n\ne -1)$. Assuming particle is at rest at origin at $t=0$, the relation between the velocity and the position$\left(r\right)$ of the particle at time $t=1\text{s}$ is

(Assume SI units)

1. $v=r$
2. $v=2r$
3. $v=\frac{(n+3)r}{2}$
4. $v=\frac{(n+1)r}{2}$