Numerical Problems : Laws of Motion

LEVEL – II

Q:1. A smooth wedge with elevation θ is fixed in an elevator moving up with uniform acceleration ao = g/2. The base of the wedge has a length L. Find the time taken by a particle sliding down the incline to reach the base.

Ans: $\displaystyle \sqrt{\frac{16 L}{3\sqrt{3} g}}$

Q:2. A body of mass 2 kg is lying on a rough inclined plane of inclination 30°. Find the magnitude of the force parallel to the incline needed to make the block move (a) up the incline
(b) down the incline. Coefficient of static friction = 0.2.

Q:3. A spring has its end fixed to the ceiling of the elevator rigidly. It has spring constant = 2000 N/m. A man of mass 50 kg climbs along the other end of the spring vertically up with an acceleration of 2 m/s2relative to the elevator. The elevator is going up with retardation 3 m/s2 . Find extension in the spring.

Ans: 0.225 m

Q:4. A bar of mass m resting on a smooth horizontal plane starts moving due to the force F = mg/3 of constant magnitude. In the process of its rectilinear motion the angle α between the direction of this force and the horizontal varies as α = as, where a is a constant, and s is the distance traversed by the bar from its initial position. Find the velocity of the bar as a function of the angle α .

Ans : $\displaystyle v = \sqrt{\frac{2 g}{3 a}sin\alpha}$

Q:5. Two blocks in contact of masses 2 kg and 4 kg in succession from down to up are sliding down an inclined surface of inclination 30° . The friction coefficient between the block of mass 2.0 kg and the inclines is μ1, and that between the block of mass 4.0 kg and the incline is μ2 . Calculate the acceleration of the 2.0 kg block if (a) μ1 = 0.20 and μ2 = 0.30 , (b) μ1 = 0.30 and μ2 = 0.20. Take g = 10 m/s2.

Ans: (a)3.27 m/s2 (b)2.97 m/s2

Q:6. A balloon is descending with a constant acceleration a , less than the acceleration due to gravity g. The weight of the balloon, with its basket and contents, is w. What weight, w should be released so that the balloon will begin to accelerate upward with constant acceleration a ? Neglect air resistance.

Q:7. In the figure shown co-efficient of friction between the block B and C is 0.4. There is no friction between the block C and the surface on which it is placed. The block A is released from rest , find the distance moved by the block C when block A descends through a height 2 m. Given masses of the blocks are mA = 3 kg, mB = 5 kg and mC = 10 kg.

Ans : Distance moved by C is 2 m only

Q:8. Two masses m1 and m2 are connected by means of a light string, that passes over a light pulley as shown in the figure. If m1 = 2kg and m2 = 5 kg and a vertical force F is applied on the pulley then find the acceleration of the masses and that of the pulley when
(a) F = 35 N (b) F = 70 N (c) F = 140 N

Ans: (a) aP = 0 and a1 = a2 = 0 (b) a1 = 15/2 m/s2 , aP = a1/2 (c) a1 = 25 m/s2 , a2 = 4 m/s2 , aP = (a1 + a2)/2

Q:9. In the given figure the co-efficient of friction between the walls of block of mass m and the plank of mass M is μ. The same co-efficient of friction is there between the plank and the horizontal floor. The force F is of 100 N and the masses m and M are of 1 kg and 3 kg respectively. Find the value of μ , if the block does not slip along the wall of the plank.

Ans: μ = 0.5

Q:10. In figure, a bar of mass m is placed on the smooth surface of a wedge of mass M. The bar is connected to an inextensible string passing over a light smooth pulley fitted with the wedge. The string is connected to the vertical wall. The angle of inclination of the slant surface of the wedge is α . If all contacting surfaces are smooth, find the acceleration of the wedge.

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