Q126
Objective
2. Assertion and reason
MCQ
Assertion: In the system of two blocks of equal masses as shown, the coefficient of friction between the blocks $(\mu_{2})$ is less than coefficient of friction $(\mu_{1})$ between lower block and ground. For all values of force F applied on upper block, lower block remains at rest.
Reason: Frictional force on lower block due to upper block is not sufficient to overcome the frictional force on lower block due to ground.
Reason: Frictional force on lower block due to upper block is not sufficient to overcome the frictional force on lower block due to ground.
A.
If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B.
If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C.
If Assertion is correct but Reason is incorrect.
D.
If Assertion is incorrect but Reason is correct.
Q127
Objective
2. Assertion and reason
MCQ
Assertion: In the figure shown, block of mass m is stationary with respect to lift. Force of friction acting on the block is greater than $mg \sin \theta$ .
Reason: If lift moves with constant velocity, then force of friction is equal to $mg \sin \theta$ .
Reason: If lift moves with constant velocity, then force of friction is equal to $mg \sin \theta$ .
A.
If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B.
If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C.
If Assertion is correct but Reason is incorrect.
D.
If Assertion is incorrect but Reason is correct.
Q128
Objective
2. Assertion and reason
MCQ
Assertion: Block A is resting on one corner of a box as shown in figure. Acceleration of box is $(2\hat{\mathbf{i}} + 2\hat{\mathbf{j}})\mathrm{ms}^{-2}$ . Let $N_{1}$ is the normal reaction on block from vertical wall and $N_{2}$ from ground to box. Then, $\frac{N_{1}}{N_{2}} = \frac{1}{6}$ . (Neglect friction)
Reason: $N_{1} = 0$ , if lift is stationary.
A.
If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B.
If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C.
If Assertion is correct but Reason is incorrect.
D.
If Assertion is incorrect but Reason is correct.
Q129
Objective
3. Statement based questions
MCQ
Which of the following statement (s) is/are correct?
A.
The weighing machine measures the weight of a body.
B.
During free fall of a person one feels weightlessness because his weight becomes zero.
C.
During free fall, the person falls with an acceleration of g.
D.
All of the above
Q130
Objective
3. Statement based questions
MCQ
Which of the following statement (s) is/are incorrect?
A.
Static friction is self-adjusting while kinetic friction is constant.
B.
Friction always opposes the motion of two bodies.
C.
Without friction, one can move on a smooth surface.
D.
Some mechanical energy is lost in the form of heat due to air friction.
Q131
Objective
3. Statement based questions
MCQ
Which of the following statement (s) is/are correct?
I. A string has a mass m. If it is accelerated,
tension is non-uniform and if it is not accelerated,
tension is uniform.
II. Tension force is an electromagnetic force.
A.
Only I
B.
Only II
C.
Both I and II
D.
None of these
Q132
Objective
3. Statement based questions
MCQ
In the diagram shown in figure, string is massless and pulley is smooth, then which of the following statement (s) is/are correct?
I. Net force on 1 kg block is $\frac{10}{3}$ N.
II. Net force on both the blocks will be same.
II. Net force on both the blocks will be same.
A.
Only I
B.
Only II
C.
Both I and II
D.
None of these
Q133
Objective
3. Statement based questions
MCQ
Two forces are acting on a rope lying on a smooth table as shown in figure.
Which of the following statement (s) is/are correct?
I. In moving from A to B, tension on string decreases from 2F to F.
II. Situation will becomes indeterminant, if we take it a massless string.
Which of the following statement (s) is/are correct?
I. In moving from A to B, tension on string decreases from 2F to F.
II. Situation will becomes indeterminant, if we take it a massless string.
A.
Only I
B.
Only II
C.
Both I and II
D.
None of these
Q134
Objective
4. Match the columns
Numerical
In the diagram shown in figure, match the following columns (Take, $g = 10 \, ms^{-2}$ )
| Column I | Column II | ||||||
| (A) | Normal reaction | (p) | 12 SI unit | ||||
| (B) | Force of friction | (q) | 20 SI unit | ||||
| (C) | Acceleration of block | (r) | zero | ||||
| (s) | 2 SI unit | ||||||
| Codes | |||||||
| A | B | C | A | B | C | ||
| (a) | p | q | r | (b) | q | p | r |
| (c) | q | p | s | (d) | p | s | r |
Correct Answer: C
Explanation:
$N = mg - 20\sqrt{2}\sin 45^{\circ} = 20\mathrm{N}, f = \mu_{k}N = 12\mathrm{N}$
Since, $20\sqrt{2}\cos45^{\circ}>\mu N$ block will move and its acceleration will be
$a = \frac {2 0 \sqrt {2} \cos 4 5 ^ {\circ} - \mu_ {k} N}{m} = \frac {2 0 - 1 2}{4} = 2 \mathrm{ms} ^ {- 2}$
Hence, A ā q, B ā p, C ā s.
Since, $20\sqrt{2}\cos45^{\circ}>\mu N$ block will move and its acceleration will be
$a = \frac {2 0 \sqrt {2} \cos 4 5 ^ {\circ} - \mu_ {k} N}{m} = \frac {2 0 - 1 2}{4} = 2 \mathrm{ms} ^ {- 2}$
Hence, A ā q, B ā p, C ā s.
Q135
Objective
4. Match the columns
Numerical
In the diagram shown in figure, match the following columns. (Take, $g = 10 \, ms^{-2}$ )
| Column I | Column II | |||||||
| (A) | Acceleration of 2 kg block | (p) 8 SI unit | ||||||
| (B) | Net force on 3 kg block | (q) 25 SI unit | ||||||
| (C) | Normal reaction between 2 kg and 1 kg | (r) 2 SI unit | ||||||
| (D) | Normal reaction between 3 kg and 2 kg | (s) 45 N | ||||||
| (t) None | ||||||||
| Codes | ||||||||
| A | B | C | D | A | B | C | ||
| (a) | q | r | t | t | (b) | p | s | r |
| (c) | s | s | p | t | (d) | r | t | q |
Correct Answer: D
Explanation:
Acceleration of system,
$a = \frac {6 0 - 1 8 - (m _ {1} + m _ {2} + m _ {3}) g \sin 3 0 ^ {\circ}}{(m _ {1} + m _ {2} + m _ {3})} = 2 \mathrm{ms} ^ {- 2}$
Net force on 3 kg block = $m_{3}a = 6N$
From free body diagram of 1 kg block, we have
$N _ {1 2} - m _ {1} g \sin 3 0 ^ {\circ} - 1 8 = m _ {1} a$
$N _ {1 2} = 2 5 \mathrm{N}$
From free body diagram of 3 kg block, we have
$a = \frac {6 0 - 1 8 - (m _ {1} + m _ {2} + m _ {3}) g \sin 3 0 ^ {\circ}}{(m _ {1} + m _ {2} + m _ {3})} = 2 \mathrm{ms} ^ {- 2}$
Net force on 3 kg block = $m_{3}a = 6N$
From free body diagram of 1 kg block, we have
$N _ {1 2} - m _ {1} g \sin 3 0 ^ {\circ} - 1 8 = m _ {1} a$
$N _ {1 2} = 2 5 \mathrm{N}$
From free body diagram of 3 kg block, we have
Q136
Objective
4. Match the columns
Numerical
In the diagram shown in figure. Match the following columns.
| Column I | Column II | ||||||
| (A) | Absolute acceleration of 1 kg block | (p) | $11 \text{ ms}^{-2}$ | ||||
| (B) | Absolute acceleration of 2 kg block | (q) | $6 \text{ ms}^{-2}$ | ||||
| (C) | Relative acceleration between the two | (r) | $17 \text{ ms}^{-2}$ | ||||
| (s) | None | ||||||
| Codes | |||||||
| A | B | C | A | B | C | ||
| (a) | p | q | r | (b) | s | p | s |
| (c) | r | q | p | (d) | p | p | r |
Correct Answer: B
Explanation:
Force diagram of both the blocks are as shown.
ā
ā
$a _ {2} = \frac {2 2}{2} = 1 1 \mathrm{m/s} ^ {2}$
ā
$a _ {2 1} = a _ {2} - a _ {1} = 7 \mathrm{m/s} ^ {2}$
Hence, A ā s, B ā p, C ā s.
ā
ā
$a _ {2} = \frac {2 2}{2} = 1 1 \mathrm{m/s} ^ {2}$
ā
$a _ {2 1} = a _ {2} - a _ {1} = 7 \mathrm{m/s} ^ {2}$
Hence, A ā s, B ā p, C ā s.
Q137
Objective
4. Match the columns
Numerical
In the diagram shown in figure, all pulleys are smooth and massless and strings are light. Match the following columns. $^{ā²}$ $E = 30 \, N$
| Column I | Column II | ||||||||
| (A) | 1 kg block | (p) | will remain stationary | ||||||
| (B) | 2 kg block | (q) | will move down | ||||||
| (C) | 3 kg block | (r) | will move up | ||||||
| (D) | 4 kg block | (s) | $5 \text{ ms}^{-2}$ | ||||||
| (t) | $10 \text{ ms}^{-2}$ | ||||||||
| Codes | |||||||||
| A | B | C | D | A | B | C | D | ||
| (a) | r,t | p | q | q,s | (b) | p | r,s | q,t | s |
| (c) | p,s | r | q,s | t | (d) | p | t | r | s |
Correct Answer: A
Explanation:
Since, the pulleys are smooth, net force on each pulley should be zero. With this concept, tensions on all strings are shown below.
Now, we can draw free body diagrams of all the four blocks.
$\mathrm{Hence}, \mathrm{A} \rightarrow (\mathrm{r}, \mathrm{t}), \mathrm{B} \rightarrow \mathrm{p}, \mathrm{C} \rightarrow \mathrm{q}, \mathrm{D} \rightarrow (\mathrm{q}, \mathrm{s}).$
Now, we can draw free body diagrams of all the four blocks.
$\mathrm{Hence}, \mathrm{A} \rightarrow (\mathrm{r}, \mathrm{t}), \mathrm{B} \rightarrow \mathrm{p}, \mathrm{C} \rightarrow \mathrm{q}, \mathrm{D} \rightarrow (\mathrm{q}, \mathrm{s}).$
Q138
Objective
5. Medical entrances' gallery
MCQ
In the figure, block A and B of masses 2m and m are connected with a string and system is hanged vertically with the help of a spring. Spring has negligible mass. Find out magnitude of acceleration of masses 2m and m just after the instant when the string of mass m is cut
A.
g, g
B.
g, g/2
C.
g/2, g
D.
g/2, g/2
Q139
Objective
5. Medical entrances' gallery
MCQ
Three identical blocks of masses m = 2 kg are drawn by a force 10.2 N on a frictionless surface. What is the tension (in newton) in the string between the blocks B and C?
A.
9.2
B.
8
C.
3.4
D.
9.8