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.

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