In the figure shown initially spring is in unstretched state and blocks are at rest. Now 100N force is applied on block A and B as shown in the figure. After some time velocity of A becomes 2m/s and that of B is 4m/s and block A displaced by amount 10cm and spring is stretched by amount 30cm. Then work done by spring (in Joule) force on A will be :
The correct answer is: -6
Starting at rest, a 5kg object is acted upon by only one force as indicated in the figure. Find the total work done (in Joule) by the force on the object :
The correct answer is: 90
A particle is projected vertically upwards with a speed of 16m/s, after some time, when it again passes through the point of projection, its speed is found to be 8m/s. It is known that the work done by air resistance is same during upward and downward motion. Then the maximum height (in m) attained by the particle is : (Take g = 10m/s2) :
From work energy theorem for upward motion
(work by air resistance) for downward motion
or h = 8m
The correct answer is: 8
A particle A of mass 10/7 kg is moving in the positive x direction. Its initial position is x = 0 and initial velocity is 1m/s. The velocity (in m/s) at x = 10 is ......... .
(use the graph given)
Area under P-x graph
The correct answer is: 4
The blocks of mass m1 = 1kg and m2 = 2kg are connected by a spring, rest on a rough horizontal surface. The spring is unstretched. The spring constant of spring is K = 2N/m. The coefficient of friction between blocks and horizontal surface is μ = 1/2. Now the left block is imparted a velocity u towards right as shown. Then what is the largest value of u (in m/s) such that the block of mass m2 never moves. (Take g = 10 m/s2)
For the block of mass m2, not to move, the maximum compression in the spring x0 should be such that
kx0 = μm2 .....(i)
Applying work energy theorem to block of mass m1 we get
From equation (1) and (2) we get
putting the appropriate value we get μ = 10m/s.
The correct answer is: 10
A block of mass m is attached with a massless spring of force constant k. The block is placed over a fixed rough inclined surface for which the coefficient of friction is μ = 3/4. The block of mass m is initially at rest. The block of mass M is released from rest with spring in unstretched state. The minimum value of M required to move the block up the plane is given by λm Find the value of λ.
(neglect mass of string and pulley and friction in pulley.)
As long as the block of mass m remains stationary, the block of mass M released from rest comes down by (before coming it rest momentarily again).
Thus the maximum extension in spring is
for block of mass m to just move up the incline
The correct answer is: 0.6
In the given figure, the magnitude of work done by frictional force on upper and lower block?
Assume 20kg and 30kg block move together
∴ friction force on 20kg block is f = 20 × 1 = 20N
The maximum value of frictional force is
Hence no slipping is occurring.
∴ The value of frictional force is f = 20N
Distance traveled in t = 2 seconds.
Work done by frictional force on upper block is
Wfriction = 20 × 2 = 40J
Work done by friction force on lower block is = –20 × 2 = –40J.
The correct answer is: 40
A fire hose has a diameter of 2.5cm and is required to direct a jet of water to a height of at least 40m. The minimum power (in kW) of the pump needed for this hose is :
The speed of the water leaving the hose must be if it is to reach a height h when directed vertically upward. If the diameter is d, the volume of water ejected at this speed is
⇒ Mass ejected is
This kinetic energy of this water leaving the hose
The correct answer is: 2.15
If there is no friction any where, the speed of the wedge, as the block leaves the wedge is :
Linear momentum is conserved only in horizontal direction.
1/2(mv1)2+1/2(mv2)2 = mgh....(ii)
A spring lies along an x-axis attached to a wall at one end and a block at the other end. The block rests on a frictionless surface at x = 0. A force of constant magnitude F is applied to the block that begins to compress the spring, until the block comes to a maximum displacement xmax.
During the displacement, which of the curves shown in the graph best represents the kinetic energy of the block.
Applying W-E theorem on the block for any compression x :
⇒ KE vs x is inverted parabola.
The correct answer is: 3