Advertisements
Advertisements
Question
A block of 2 kg is suspended from a ceiling by a massless spring of spring constant k = 100 N/m. What is the elongation of the spring? If another 1 kg is added to the block, what would be the further elongation?
Advertisements
Solution
Given,
mass of the first block, m = 2 kg
k = 100 N/m
Let elongation in the spring be x. 
From the free-body diagram,
kx = mg
\[x = \frac{mg}{k} = \frac{2 \times 9 . 8}{100}\]
\[ = \frac{19 . 6}{100} = 0 . 196 \approx 0 . 2 m\]
Suppose, further elongation, when the 1 kg block is added, is \[∆ x\] Then, \[k\left( x + ∆ x \right) = m'g\]
⇒ k \[∆ x\] 3g − 2g = g
\[\Rightarrow ∆ x = \frac{g}{k} = \frac{9 . 8}{100} = 0 . 098 \approx 0 . 1 m\]
APPEARS IN
RELATED QUESTIONS
When a carpet is beaten with a stick, dust comes out of it. Explain.
If the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly describes the trajectory of the stone after the string breaks?
Fill in the following blank with suitable word :
Newton’s first law of motion is also called Galileo’s law of ………………………
State Newton’s first law of motion. Give two examples to illustrate Newton’s first law of motion.
Find the acceleration produced by a force of 5 N acting on a mass of 10 kg.
The acceleration of a particle is zero, as measured from an inertial frame of reference. Can we conclude that no force acts on the particle?
Consider a book lying on a table. The weight of the book and the normal force by the table in the book are equal in magnitude and opposite in direction. Is this an example of Newton's third law?
A particle stays at rest as seen in a frame. We can conclude that
(a) the frame is inertial
(b) resultant force on the particle is zero
(c) the frame may be inertial but the resultant force on the particle is zero
(d) the frame may be non-inertial but there is a non-zero resultant force
If you jump barefoot on a hard surface, your legs are injured. But they are not injured if you jump on a soft surface like sand or pillow. Why?
An object of mass 2 kg is sliding with a constant velocity of 4 m/s on a frictionless horizontal table. The force required to keep this object moving with the same velocity is :
Give one example each of inertia of rest and inertia of motion.
The amount of inertia of a body depends on its _________.
A man riding on a car has ___________ Inertia.
When a bus suddenly takes a tum, the passengers are thrown outwards because of
A body of mass 10 kg is acted upon by two perpendicular forces, 6 N and 8 N. The resultant acceleration of the body is ______.
- 1 m s–2 at an angle of tan−1 `(4/3)` w.r.t 6 N force.
- 0.2 m s–2 at an angle of tan−1 `(4/3)` w.r.t 6 N force.
- 1 m s–2 at an angle of tan−1 `(3/4)` w.r.t 8 N force.
- 0.2 m s–2 at an angle of tan−1 `(3/4)` w.r.t 8 N force.
In a legend, the hero-kid kicked a toy pig so that it is projected with a speed greater than that of its cry. If the weight of the toy pig is assumed to be 5 kg and the time of contact 0.01 sec., the force with which the hero-kid kicked him was ______.
(Speed of cry = 330 m/s)
When does an object accelerate?
An interstellar spacecraft, far away from the influence of any star or planet, is moving at high speed under the influence of fusion rockets (due to the thrust exerted by fusion rockets, the spacecraft is accelerating). Suddenly the engine malfunctions and stops. The spacecraft will ______.
