CBSE Class 11 Physics Work Energy Power Basic Problems

BASIC LEVEL ASSIGNMENT

1. A small disc of mass m slides down a smooth hill of height h without initial velocity and gets onto a plank of mass M lying on the horizontal plane at the base of hill as shown in the figure. Due to friction between the disc and the plank, disc slows down and beginning with a certain moment, moves in one piece with the plank. Find out total work performed by the frictional forces in this process.

2. A block of mass m starts from rest to slide along a smooth frictionless track of the shape shown in the figure. What should be height h so that when the mass reaches point A on the track, it pushes the track with a force equal to thrice its weight ?

3. Two blocks of masses m₁ = 2 kg and m₂ = 5 kg are moving in the same direction along a frictionless surface with speeds 10 m/s and 3 m/s respectively, m₂ being ahead of m_1. An ideal spring with k = 1120 N/m is attached to the back side of m₂. Find the maximum compression of the spring when the blocks collide.

4. An automobile of mass m accelerates, starting from rest, while the engine supplies constant power P ; show that :
(a) The velocity is given as a function of time by v = (2 Pt/m)1/2
(b) The position is given as a function of time by s = (8 P/9m)1/2 t3/2.

5. A massless platform is kept on a light elastic spring, as shown in the figure. When a sand particle of mass 0.1 kg is dropped on the pan from a height of 0.2 m, the particle strikes the pan and sticks to it while the spring compresses by 0.01 m. From what height should the particle be dropped to cause a compression of 0.04 m ?

6. A spring gun has spring constant 100 N/m. A small ball of mass 0.1 kg is put in its barrel by compressing the spring through 0.05 m as shown in the figure

(a) Find the velocity of the ball when the spring acquires normal after length after being released.
(b) Where should a box be placed on the ground so that the ball falls in it, if the ball leaves the gun horizontally at a height of 2 m above the ground ? (g = 10 m/s²)

7. Two blocks are connected by a string as shown in the figure. They are released from rest. Show that after they have moved a distance L, their common speed is given by√2(m₂-μm₁)gL/(m₁+m₂)
where μ is the coefficient of friction between the floor and the blocks.

8. A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac is varying with time t as ac = k² rt² when k is a constant. What is the power delivered to the particle by the forces acting on it ?

9. A stone with weight w is thrown vertically upward into the air with initial speed v0. If a constant force f due to air drag acts on the stone throughout its flight :
(a) Show that the maximum height reached by the stone is h = v²/2 g[1 +( f/w )]
(b) Show that the speed of the stone upon impact with the ground is v = v₀(w-f/w+f)^1/2

10. One end of a spring of natural length h is fixed at the ground and the other end is fitted with a smooth ring of mass m which is allowed to slide on a horizontal rod fixed at a height h as shown in figure. Initially, the spring makes an angle of 37º with the vertical when the system is released from rest. Find the speed of the ring when the spring becomes vertical.