Force and Laws of Motion
(take g = 10 ms–2)
The pulley is frictionless and of negligible mass. The downward acceleration of mass m1 is
(Assume m1 = m2 = m3 = m)
[Useful information: tan (5.5°) ≈ 0.1; tan (11.5°) ≈ 0.2; tan (16.5°) ≈ 0.3]
|List I||List II|
|P.||θ = 5°||1.||m2gsin θ|
|Q.||θ = 10°||2.||(m1 + m2)gsin θ|
|R.||θ = 15°||3.||μm2gcos θ|
|S.||θ = 20°||4.||μ(m1 + m2)gcos θ|
A hoop of radius r and mass m rotating with and angular velocity ω0 is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?
Three blocks with masses m, 2 m and 3 m are connected by strings, as shown in the figure. After an upward force F is applied on block m, the masses move upward at constant speed v. What is the net force on the block of mass 2 m?
(g is the acceleration due to gravity)
The upper half of an inclined plane of inclination θ is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by:
An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 ms−1 and the second part of mass 2 kg moves with 8 ms−1 speed. If the third part flies off with 4 ms−1 speed, then its mass is:
Reason: Vector sum of all the external forces is zero.
Reason To every action there is an equal and opposite reaction.
A small block of mass of 0.1 kg lies on fixed inclined plane PQ which makes an angle with the horizontal. A horizontal force of 1 N acts on the block though its centre of mass as shown in the figure. The block remains stationary if (Take g = 10 )
A car of mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. If the banking angle is 45°, the speed of the car is:
A ball of mass (m) 0.5 kg is attached to the end of a string having length (L) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in radian/s) is:
A block is moving on an inclined plane making an angle 45o with the horizontal and the coefficient of friction is . The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define N = 10, then N is
Reason : Thrust also depends upon exhaust speed of the gases.
A boy is pushing a ring of mass 2 kg and radius 0.5m with a stick as shown in the figure. The stick applies a force of 2 N on the ring and rolls it without slipping with an acceleration of 0.3 ms−2. The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is (P/10). The value of P is.
Reason : They do not act at the same time.
Reason: The momentum is greater in the first case.
A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, travelling with a velocity in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity V of the bullet is:
A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity. A small ball of mass 0.1 kg moving with velocity in the opposite direction hits the ring at a height of 0.75 m and goes vertically up with velocity. Immediately after the collision,
A series R-C circuit is connected to AC voltage source. Consider two cases; (a) when C is without a dielectric medium and b when C is filled with dielectric of constant k. The current of the following is/are true?
Reason : The bending angle from the vertical would decrease with increase in velocity.
A block of mass m is on an inclined plane of angle. The coefficient of friction between the block and the plane is and tan. The block is held stationary by applying a force P parallel to the plane. The direction of force pointing up the plane is taken to be positive. As P is varied from
P1 = mg (sin), the frictional force f versus p graph will look like
Reason : To every action there is an equal and opposite reaction.
Reason: For every action there is an equal and opposite reaction.
Reason Small sized wooden sleepers are used so that rails exert more pressure on the railway track. Due to which rail does not leave the track.
A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg. Taking find the work done (in joules) by the string on the block of mass 0.36 kg during the first second after the system is released from rest.
It is easier to pull a heavy object than to push it on a level ground.
STATEMENT − 2
The magnitude of frictional force depends on the nature of the two surfaces in contact
(a) the time after which the front faces of both the blocks come in the same line
(b) the distance covered by each block for attaining the above position
(a) The motion of the ball is observed from the frame of the trolley. Calculate the angle Φ made by the velocity vector of the ball with the x-axis in this frame.
(b) Find the speed of the ball with respect to the surface, if Φ = 4θ/3.
(B) (m1 + m2) gt0
(C) 2(m1 + m2) gt0
(D) 1/2(m1 + m2) gt0
At t0, the second cannon ball is fired. Assume that the resistive force between the rails and the carriage is constant and ignore the vertical motion of the carriage throughout. If the second ball also hits and sticks to the carriage, what will be the horizontal velocity of the carriage just after the second impact?