Advertisements
Advertisements
प्रश्न
Both the springs shown in the following figure are unstretched. If the block is displaced by a distance x and released, what will be the initial acceleration?
उत्तर
Let the block m be displaced towards left by displacement x.
\[\therefore F_1 = -K_1X\] (compressed)
\[ F_2 = -K_2X\] (expanded)
\[ma = F_1 + F_2\]
\[\Rightarrow a = \frac{- x\left( k_1 + k_2 \right)}{m}\]
i.e. \[\left( k_1 + k_2 \right)\frac{x}{m}\] opposite the displacement or towards the mean position.
APPEARS IN
संबंधित प्रश्न
Two blocks of equal mass m are tied to each other through a light string. One of the blocks is pulled along the line joining them with a constant force F. Find the tension in the string joining the blocks.
In the following figure shows a uniform rod of length 30 cm and mass 3.0 kg. The strings shown in the figure are pulled by constant forces of 20 N and 32 N. Find the force exerted by the 20 cm part of the rod on the 10 cm part. All the surfaces are smooth and the strings and the pulleys are light.
Let m1 = 1 kg, m2 = 2 kg and m3 = 3 kg in the following figure. Find the accelerations of m1, m2 and m3. The string from the upper pulley to m1 is 20 cm when the system is released from rest. How long will it take before m1 strikes the pulley?
A monkey is climbing on a rope that goes over a smooth light pulley and supports a block of equal mass at the other end in the following figure. Show that whatever force the monkey exerts on the rope, the monkey and the block move in the same direction with equal acceleration. If initially both were at rest, their separation will not change as time passes.
A body of mass m moving with a velocity v is acted upon by a force. Write an expression for change in momentum in each of the following cases: (i) When v << c, (ii) When v → c and (iii) When v << c but m does not remain constant. Here, c is the speed of light.
Show that the rate of change of momentum = mass × acceleration. Under what condition does this relation hold?
Two balls A and B of masses m and 2 m are in motion with velocities 2v and v, respectively. Compare:
(i) Their inertia.
(ii) Their momentum.
(iii) The force needed to stop them in the same time.
A force of 10 N acts on a body of mass 2 kg for 3 s, initially at rest. Calculate : The velocity acquired by the body
State the magnitude and direction of the force of gravity acting on the body of mass 5 kg. Take g = 9.8 m s-2.
A pebble is thrown vertically upwards with a speed of 20 m s-1. How high will it be after 2 s? (Take g = 10 m s-2)
A pebble is dropped freely in a well from its top. It takes 20 s for the pebble to reach the water surface in the well. Taking g = 10 m s-2 and speed of sound = 330 m s-1. Find : The time when echo is heard after the pebble is dropped.
Prove mathematically F = ma
Multiple Choice Question. Select the correct option.
The impulse of a body is equal to:
State Newton's second law of motion. Is Newton's first law of motion contained in Newton's second law of motion?
A ball is thrown upward and reaches a maximum height of 19.6 m. Find its initial speed?
The INCORRECT statement about Newton's second law of motion is
A metre scale is moving with uniform velocity. This implies ______.
The position time graph of a body of mass 2 kg is as given in figure. What is the impulse on the body at t = 0 s and t = 4 s.
Why does a child feel more pain when she falls down on a hard cement floor, than when she falls on the soft muddy ground in the garden?
A woman throws an object of mass 500 g with a speed of 25 ms1.
- What is the impulse imparted to the object?
- If the object hits a wall and rebounds with half the original speed, what is the change in momentum of the object?
