# Displacement, Velocity and Acceleration

 Question 1
The wheels and axle system lying on a rough surface is shown in the figure.

Each wheel has diameter 0.8 m and mass 1 kg. Assume that the mass of the wheel is concentrated at rim and neglect the mass of the spokes. The diameter of axle is 0.2 m and its mass is 1.5 kg. Neglect the moment of inertia of the axle and assume $g=9.8 m/s^2$. An effort of 10 N is applied on the axle in the horizontal direction shown at mid span of the axle. Assume that the wheels move on a horizontal surface without slip. The acceleration of the wheel axle system in horizontal direction is ________$m/s^2$(round off to one decimal place).
 A 2.8 B 3.6 C 5 D 6.4
GATE ME 2021 SET-2   Theory of Machine
Question 1 Explanation:

\begin{aligned} I_G&=2 \times (M \times r^2) \\&=2 \times 1 \times 0.4^2=0.32\; kg/m^2 \\ \Sigma F&=m\cdot a\\ &\Rightarrow 10-f=3.5 \times a\;...(i)\\ \Sigma T&=I\cdot \alpha \\ &\Rightarrow 10 \times 0.1 -f\times 0.4=0.32 \times \frac{a}{0.4} \;...(ii)\\ \end{aligned}
[As there is no slip $\therefore \;\;a=r\alpha$ ]
Solving (i) and (ii),
$\therefore \;\;a=5\; m/s^2$
 Question 2
Consider the mechanism shown in the figure. There is rolling contact without slip between the disc and ground.

Select the correct statement about instantaneous centers in the mechanism.
 A Only points P, Q, and S are instantaneous centers of mechanism B Only points P, Q, S and T are instantaneous centers of mechanism C Only points P, Q, R, S, and U are instantaneous centers of mechanism D All points P, Q, R, S, T and U are instantaneous centers of mechanism
GATE ME 2021 SET-2   Theory of Machine
Question 2 Explanation:

Points P, Q, R, S, T and U are instantaneous centers of mechanism.

 Question 3
The number of qualitatively distinct kinematic inversions possible for a Grashof chain with four revolute pairs is
 A 1 B 2 C 3 D 4
GATE ME 2020 SET-2   Theory of Machine
Question 3 Explanation:
They are:
1. Double crank mechanism
2. Crank-rocker mechanism
3. Double rocker mechanism
 Question 4
The 2 kg block shown in figure (top view) rests on a smooth horizontal surface and is attached to a massless elastic cord that has a stiffness 5 N/m.

The cord hinged at $O$ is initially unstretched and always remains elastic. The block is given a velocity $v$ of 1.5 m/s perpendicular to the cord. The magnitude of velocity in m/s of the block at the instant the cord is stretched by 0.4 m is
 A 0.83 B 1.07 C 1.36 D 1.5
GATE ME 2020 SET-1   Theory of Machine
Question 4 Explanation:
Energy conservation
\begin{aligned} \frac{1}{2} m V_{1}^{2} &=\frac{1}{2} m V_{0}^{2}+\frac{1}{2} k x^{2} \\ \Rightarrow \quad 2 \times 1.5^{2} &=2 \times V_{0}^{2}+5 \times 0.4^{2} \\ V_{0} &=1.360 \mathrm{m} / \mathrm{s} \end{aligned}
 Question 5
A four bar mechanism is shown below

For the mechanism to be a crank-rocker mechanism, the length of the link PQ can be
 A 80 mm B 200 mm C 300 mm D 350 mm
GATE ME 2020 SET-1   Theory of Machine
Question 5 Explanation:

For Crank-Rocker mechanism, shortest link must be crank and adjacent to fixed as well as Grashoff's law must be satisfied.
If $l = 80 mm$ then shortest will be = 80 mm
as well as (80 + 600) $\lt$(400 + 300)
680 $\lt$ 700
Therefore law is satisfied.
$\Rightarrow$ l = 80 mm

There are 5 questions to complete.

### 2 thoughts on “Displacement, Velocity and Acceleration”

1. Sir,7 the question som pyq present plz change otherwise great sir this practice sheet