Motion in A Straight Line Test

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Motion in A Straight Line Test - 70

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Question 1
1 / -0

In the system shown in figure $$m_A = 4m, m_B = 3 m$$ and $$m_C = 8 m$$. Friction is absent everywhere. String is light and in-extensible. If the system is released from rest find the acceleration of block B

A
$$\dfrac{g}{8}$$ (leftward)

B
$$\dfrac{g}{2}$$ (leftward)

C
$$\dfrac{g}{6}$$ (rightward)

D
$$\dfrac{g}{4}$$ (rightward)

Solution

When the system is released from the position of rest, the equations of motions are given as,

$$4a = 4g - T$$ (1)

$$T = 3a$$ (2)

From the equation (1) and (2) it can be written as,

$$7a = 4g$$

$$a = \dfrac{{4g}}{7}$$

$$a \approx \dfrac{g}{2}$$

Thus, the acceleration of block B is $$\dfrac{g}{2}$$ towards the left side.
Question 2
1 / -0

A particle initially at rest is subjected to two forces. One is constant, the other is a retarding force proportion at to the particle velocity. In the subsequent motion of the particle.

A
The acceleration will increase from zero to a constant value.

B
The acceleration will decrease from its initial value to a zero.

C
The velocity will increase from zero to a maximum & then decrease.

D
The velocity will increase from zero to a constant value.

Solution

Let,
Constant force $$=K_1$$
Variable force $$=-K_2V$$
Net Force $$F=K_1-K_2V$$
Acceleration $$a=\dfrac{K_1-K_2V}{m}$$
As the velocity increases the net force will decrease. When both retarding and constant forces become equal then net force is zero. Hence the velocity is maximum and acceleration will increase from zero to constant.
Question 3
1 / -0

A body is projected vertically up at t = 0 with a velocity of 98 m/s. Another body is projected from the same point with same velocity after 4 seconds. Both bodies will meet at t =

A
6 s

B
8 s

C
10 s

D
12 s

Solution

Both the bodies have been thrown with same initial velocity
So, $$h_1 = h_2$$

Time of flight form for 1st body = t seccond
and for 2nd body = (t- 4) second (because it is projected 4sec later)

SO, $$h_1 = h_2$$
$$ut - \dfrac{1}{2} gt^2 = 4(t - 4) - \dfrac{1}{2}g (T - 4)^2$$

By solving the equation
$$t = 12 second$$

Hence (D) option is correct.
Question 4
1 / -0

A $$30\ kg $$ block rests on a rough horizontal surface. A force of $$200\ N $$ is applied on the block. The block acquires a speed of $$ 4\ m/s $$ , starting from rest in $$2\ s$$ . What is the value of coefficient of friction?

A
$$ {10}/{3} $$

B
$$ {\sqrt 3}/{10} $$

C
$$ 0.47 $$

D
$$ 0.185 $$

Solution

The acceleration is given as

$$v = u + at$$

$$a = 2\;m/{s^2}$$

The force applied on the horizontal surface is such that it just overcome the static friction

$$F - \mu N = ma$$

$$200 - \mu \cdot 30 \cdot 10 = 30 \times 2$$

The static friction is$$0.47$$
Question 5
1 / -0

The driver of a train. A travelling at a speed of $$60 \ km/h$$ applies brakes and brakes and retards the train uniformly. The train stops in $$5 \ s$$, another train $$B$$ is travelling on the parallel track with a speed of $$36 \ kmph$$. This driver also applied the brakes and the train retards uniformly. The train $$B$$ stops in $$10 \ s$$ then distance travelled by each train after the brakes were applied is:

A
$$d_A = 41.6 m, d_B = 50 m$$

B
$$d_A = 42.6 m, d_B = 20 m$$

C
$$d_B = 50 m, d_A = 41.6 m$$

D
$$d_B = 80 m, d_A = 50 m$$

Solution
Question 6
1 / -0

A body starting from rest is moving with a uniform acceleration $$5m/s^2$$ fro time $$10s$$ and after that with uniform acceleration $$10m/s^2$$ for time $$15s$$ then

A
Average acceleration of the body is $$7.5 m/s^2$$

B
Average acceleration of the body is $$8.0 m/s^2$$

C
total distance travelled by body is $$1875m$$

D
total distance travelled by body is $$2125m$$

Solution
Question 7
1 / -0

An object performs upwards journey under gravity in time $$t$$ . The downwards journey is performed in time

A
$$t$$

B
$$t^2$$

C
$$2t$$

D
$$t/2$$
Question 8
1 / -0

The times taken by a block wood (initially at rest ) to slide down a smooth inclined plane $$9.8m$$ long (angle of inclination is $$30^o$$) is

A
$$\dfrac{1}{2}s$$

B
$$1s$$

C
$$2s$$

D
$$4s$$

Solution
Question 9
1 / -0

A lift initial at rest top floor of a building moves downwards with a constant speed of $$5/ms$$ for first $$8s$$ . Therefore the support ropes are cut . The time taken by the lift to reach the ground floor from the instant its ropes were cut is. [take $$g=10m/s^2$$ and height of building $$=100m$$]

A
$$4s$$

B
$$3s$$

C
$$2s$$

D
$$5s$$

Solution
Question 10
1 / -0

A block rests on a truck moving with a velocity of $$2m/s$$. The coefficient of friction between box and truck is 0.1 . The driver applies the brake, and the truck starts to decelerate uniformly and stops in $$s$$. The total distance travelled by the box w.r.t the truck is

A
$$0.75\ m$$

B
$$0.375\ m$$

C
$$1. 5\ m$$

D
$$2\ m$$

Solution