Advertisements
Advertisements
प्रश्न
Find the acceleration of the 500 g block in the following figure.
Advertisements
उत्तर
Given:
m1 = 100 g = 0.1 kg
m2 = 500 g = 0.5 kg
m3 = 50 g = 0.05 kg
The free-body diagram for the system is shown below:
From the free-body diagram of the 500 g block,
T + 0.5a − 0.5g = 0 ...(i)
From the free-body diagram of the 50 g block,
T1 + 0.05g − 0.05a = a ...(ii)
From the free-body diagram of the 100 g block,
T1 + 0.1a − T + 0.5g = 0 ...(iii)
From equation (ii),
T1 = 0.05g + 0.05a ...(iv)
From equation (i),
T1 = 0.5g − 0.5a ...(v)
Equation (iii) becomes
T1 + 0.1a − T + 0.05g = 0
From equations (iv) and (v), we get:
0.05g + 0.05a + 0.1a − 0.5g + 0.5a + 0.05g = 0
0.65a = 0.4 g
\[\Rightarrow a = \frac{0 . 4}{0 . 65}g\]
\[ = \frac{40}{65}g = \frac{8}{13}g \left(\text{ downward }\right)\]
So, the acceleration of the 500 gm block is
\[\frac{8g}{13}\] downward.
APPEARS IN
संबंधित प्रश्न
A body of mass 0.40 kg moving initially with a constant speed of 10 m s–1 to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, the position of the body at that time to be x = 0, and predict its position at t = –5 s, 25 s, 100 s.
An aircraft executes a horizontal loop at a speed of 720 km/h with its wings banked at 15°. What is the radius of the loop?
A spy jumps from an airplane with his parachute. The spy accelerates downward for some time when the parachute opens. The acceleration is suddenly checked and the spy slowly falls to the ground. Explain the action of the parachute in checking the acceleration.
A smooth wedge A is fitted in a chamber hanging from a fixed ceiling near the earth's surface. A block B placed at the top of the wedge takes time T to slide down the length of the wedge. If the block is placed at the top of the wedge and the cable supporting the chamber is broken at the same instant, the block will.
The figure shows the displacement of a particle going along the X-axis as a function of time. The force acting on the particle is zero in the region
(a) AB
(b) BC
(c) CD
(d) DE
In a TV picture tube, electrons are ejected from the cathode with negligible speed and they attain a velocity of 5 × 106 m/s in travelling one centimetre. Assuming straight-line motion, find the constant force exerted on the electrons. The mass of an electron is 9.1 × 10−31 kg.
The force of buoyancy exerted by the atmosphere on a balloon is B in the upward direction and remains constant. The force of air resistance on the balloon acts opposite the direction of velocity and is proportional to it. The balloon carries a mass M and is found to fall to the earth's surface with a constant velocity v. How much mass should be removed from the balloon so that it may rise with a constant velocity v?
A force \[\vec{F} = \vec{v} \times \vec{A}\] is exerted on a particle in addition to the force of gravity, where \[\vec{v}\] is the velocity of the particle and \[\vec{A}\] is a constant vector in the horizontal direction. With what minimum speed, a particle of mass m be projected so that it continues to move without being defelected and with a constant velocity?
In a simple Atwood machine, two unequal masses m1 and m2 are connected by a string going over a clamped light smooth pulley. In a typical arrangement (In the following figure), m1 = 300 g and m2 = 600 g. The system is released from rest. (a) Find the distance travelled by the first block in the first two seconds; (b) find the tension in the string; (c) find the force exerted by the clamp on the pulley.
In the following figure, m1 = 5 kg, m2 = 2 kg and F = 1 N. Find the acceleration of either block. Describe the motion of m1 if the string breaks but F continues to act.
Calculate the tension in the string shown in the following figure. The pulley and the string are light and all the surfaces are frictionless. Take g = 10 m/s2.
An aeroplane is moving uniformly at a constant height under the action of two forces (i) Upward force (lift) and (ii) Downward force (weight). What is the net force on the aeroplane?
Use Newton's second law of motion to explain the following instance :
An athlete prefers to land on sand instead of hard floor while taking a high jump .
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 depth of water surface
Calculate the velocity of a body of mass 0.5 kg, when it has a linear momentum of 5 Ns.
Prove mathematically F = ma
Multiple Choice Question. Select the correct option.
Which of the following are vector quantities?
What causes motion in a body?
State Newton's second law of motion. Is Newton's first law of motion contained in Newton's second law of motion?
A body of mass 2 kg travels according to the law x(t) = pt + qt2 + rt3 where p = 3 ms−1, q = 4 ms−2 and r = 5 ms−3. The force acting on the body at t = 2 seconds is ______.
