NCERT Exemplar: Motion in a Plane | Physics Class 11 - NEET PDF Download

 Page 1


 
 
   
   
 
   
 
Multiple Choice Questions (Type-I) 
4.1. The angle between A i j =+ and B i j - = is 
(a) 45 ° 
(b) 90 ° 
(c) -45 °c 
(d) 180 ° 
Ans: Since we know that, the angle between two vectors is given by 
cos
AB
AB
?
?
?= 
Hence, 
 
i.e. 
 
Hence, the correct answer is (b). 
 
4.2. Which one of the following statements is true? 
(a) A scalar quantity is the one that is conserved in a process. 
(b) A scalar quantity is the one that can never take negative values. 
Page 2


 
 
   
   
 
   
 
Multiple Choice Questions (Type-I) 
4.1. The angle between A i j =+ and B i j - = is 
(a) 45 ° 
(b) 90 ° 
(c) -45 °c 
(d) 180 ° 
Ans: Since we know that, the angle between two vectors is given by 
cos
AB
AB
?
?
?= 
Hence, 
 
i.e. 
 
Hence, the correct answer is (b). 
 
4.2. Which one of the following statements is true? 
(a) A scalar quantity is the one that is conserved in a process. 
(b) A scalar quantity is the one that can never take negative values. 
 
 
   
(c) A scalar quantity is the one that does not vary from one point to another 
in space. 
(d) A scalar quantity has the same value for observers with different 
orientations of the axes. 
Ans: A scalar quantity has no direction hence it is the same when observed with 
different orientations of the axes. 
Hence, the correct answer is (d). 
 
4.3. Figure shows the orientation of two vectors u and v in the X-Y plane. 
If u ai bj =+ and v pi qj =+ , 
Which of the following is correct? 
 
(a) a and p are positive while b and q are negative. 
(b) a, p and b are positive while q is negative. 
(c) a, q and b are positive while p is negative. 
(d) a, b, p and q are all positive. 
Page 3


 
 
   
   
 
   
 
Multiple Choice Questions (Type-I) 
4.1. The angle between A i j =+ and B i j - = is 
(a) 45 ° 
(b) 90 ° 
(c) -45 °c 
(d) 180 ° 
Ans: Since we know that, the angle between two vectors is given by 
cos
AB
AB
?
?
?= 
Hence, 
 
i.e. 
 
Hence, the correct answer is (b). 
 
4.2. Which one of the following statements is true? 
(a) A scalar quantity is the one that is conserved in a process. 
(b) A scalar quantity is the one that can never take negative values. 
 
 
   
(c) A scalar quantity is the one that does not vary from one point to another 
in space. 
(d) A scalar quantity has the same value for observers with different 
orientations of the axes. 
Ans: A scalar quantity has no direction hence it is the same when observed with 
different orientations of the axes. 
Hence, the correct answer is (d). 
 
4.3. Figure shows the orientation of two vectors u and v in the X-Y plane. 
If u ai bj =+ and v pi qj =+ , 
Which of the following is correct? 
 
(a) a and p are positive while b and q are negative. 
(b) a, p and b are positive while q is negative. 
(c) a, q and b are positive while p is negative. 
(d) a, b, p and q are all positive. 
 
 
   
Ans: Since a, b and p, q are the components of X and Y direction and we can 
see that the second vector moving down and forwards, hence the Y-component 
of vector v , i.e. q is negative. The rest are positive. 
Hence, the correct answer is (b). 
 
4.4. The component of vector r along X-axis will have maximum value if: 
(a) r
 
is along the positive Y-axis. 
(b) r
 
is along the positive X-axis. 
(c) r
 
makes an angle of 45 ° with X-axis. 
(d) r
 
is along the negative Y-axis. 
Ans: Since the value of 
max
cos 1 ? = occurs when 0 ? =? , therefore  it can 
happen only when r is along the positive X-axis. 
Hence, the correct answer is (b). 
 
4.5. The horizontal range of a projectile fired at an angle of 15 ° is 50m. If it 
is fired with the same at an angle of 45 °, its range will be: 
(a) 60 m 
(b) 71 m 
(c) 100 m 
(d) 141 m 
Ans: Given that the horizontal range is 50m. 
Therefore, we have 
 
Page 4


 
 
   
   
 
   
 
Multiple Choice Questions (Type-I) 
4.1. The angle between A i j =+ and B i j - = is 
(a) 45 ° 
(b) 90 ° 
(c) -45 °c 
(d) 180 ° 
Ans: Since we know that, the angle between two vectors is given by 
cos
AB
AB
?
?
?= 
Hence, 
 
i.e. 
 
Hence, the correct answer is (b). 
 
4.2. Which one of the following statements is true? 
(a) A scalar quantity is the one that is conserved in a process. 
(b) A scalar quantity is the one that can never take negative values. 
 
 
   
(c) A scalar quantity is the one that does not vary from one point to another 
in space. 
(d) A scalar quantity has the same value for observers with different 
orientations of the axes. 
Ans: A scalar quantity has no direction hence it is the same when observed with 
different orientations of the axes. 
Hence, the correct answer is (d). 
 
4.3. Figure shows the orientation of two vectors u and v in the X-Y plane. 
If u ai bj =+ and v pi qj =+ , 
Which of the following is correct? 
 
(a) a and p are positive while b and q are negative. 
(b) a, p and b are positive while q is negative. 
(c) a, q and b are positive while p is negative. 
(d) a, b, p and q are all positive. 
 
 
   
Ans: Since a, b and p, q are the components of X and Y direction and we can 
see that the second vector moving down and forwards, hence the Y-component 
of vector v , i.e. q is negative. The rest are positive. 
Hence, the correct answer is (b). 
 
4.4. The component of vector r along X-axis will have maximum value if: 
(a) r
 
is along the positive Y-axis. 
(b) r
 
is along the positive X-axis. 
(c) r
 
makes an angle of 45 ° with X-axis. 
(d) r
 
is along the negative Y-axis. 
Ans: Since the value of 
max
cos 1 ? = occurs when 0 ? =? , therefore  it can 
happen only when r is along the positive X-axis. 
Hence, the correct answer is (b). 
 
4.5. The horizontal range of a projectile fired at an angle of 15 ° is 50m. If it 
is fired with the same at an angle of 45 °, its range will be: 
(a) 60 m 
(b) 71 m 
(c) 100 m 
(d) 141 m 
Ans: Given that the horizontal range is 50m. 
Therefore, we have 
 
 
 
   
Hence, 
 
That gives, 
 
Now if we have 45 ?=? , then 
 
Hence, the correct answer is (c). 
 
4.6. Consider the quantities, pressure, power, energy impulse, gravitational 
potential, electric charge, temperature, area. Out of these, the only vector 
quantities are: 
(a) Impulse, pressure and area 
(b) Impulse and area 
(c) Area and gravitational constant 
(d) Impulse and pressure 
Ans: In the above given quantities, only energy impulse and area are vector 
quantities and the rest are scalar quantities as they have no direction. 
Hence, the correct answer is (b). 
 
4.7. In a two-dimensional motion, instantaneous speed v? is positive, 
constant. Then which of the following are necessarily true? 
(a) The average velocity is not zero at any time. 
(b) Average acceleration must always vanish. 
(c) Displacements in equal time intervals are equal. 
Page 5


 
 
   
   
 
   
 
Multiple Choice Questions (Type-I) 
4.1. The angle between A i j =+ and B i j - = is 
(a) 45 ° 
(b) 90 ° 
(c) -45 °c 
(d) 180 ° 
Ans: Since we know that, the angle between two vectors is given by 
cos
AB
AB
?
?
?= 
Hence, 
 
i.e. 
 
Hence, the correct answer is (b). 
 
4.2. Which one of the following statements is true? 
(a) A scalar quantity is the one that is conserved in a process. 
(b) A scalar quantity is the one that can never take negative values. 
 
 
   
(c) A scalar quantity is the one that does not vary from one point to another 
in space. 
(d) A scalar quantity has the same value for observers with different 
orientations of the axes. 
Ans: A scalar quantity has no direction hence it is the same when observed with 
different orientations of the axes. 
Hence, the correct answer is (d). 
 
4.3. Figure shows the orientation of two vectors u and v in the X-Y plane. 
If u ai bj =+ and v pi qj =+ , 
Which of the following is correct? 
 
(a) a and p are positive while b and q are negative. 
(b) a, p and b are positive while q is negative. 
(c) a, q and b are positive while p is negative. 
(d) a, b, p and q are all positive. 
 
 
   
Ans: Since a, b and p, q are the components of X and Y direction and we can 
see that the second vector moving down and forwards, hence the Y-component 
of vector v , i.e. q is negative. The rest are positive. 
Hence, the correct answer is (b). 
 
4.4. The component of vector r along X-axis will have maximum value if: 
(a) r
 
is along the positive Y-axis. 
(b) r
 
is along the positive X-axis. 
(c) r
 
makes an angle of 45 ° with X-axis. 
(d) r
 
is along the negative Y-axis. 
Ans: Since the value of 
max
cos 1 ? = occurs when 0 ? =? , therefore  it can 
happen only when r is along the positive X-axis. 
Hence, the correct answer is (b). 
 
4.5. The horizontal range of a projectile fired at an angle of 15 ° is 50m. If it 
is fired with the same at an angle of 45 °, its range will be: 
(a) 60 m 
(b) 71 m 
(c) 100 m 
(d) 141 m 
Ans: Given that the horizontal range is 50m. 
Therefore, we have 
 
 
 
   
Hence, 
 
That gives, 
 
Now if we have 45 ?=? , then 
 
Hence, the correct answer is (c). 
 
4.6. Consider the quantities, pressure, power, energy impulse, gravitational 
potential, electric charge, temperature, area. Out of these, the only vector 
quantities are: 
(a) Impulse, pressure and area 
(b) Impulse and area 
(c) Area and gravitational constant 
(d) Impulse and pressure 
Ans: In the above given quantities, only energy impulse and area are vector 
quantities and the rest are scalar quantities as they have no direction. 
Hence, the correct answer is (b). 
 
4.7. In a two-dimensional motion, instantaneous speed v? is positive, 
constant. Then which of the following are necessarily true? 
(a) The average velocity is not zero at any time. 
(b) Average acceleration must always vanish. 
(c) Displacements in equal time intervals are equal. 
 
 
   
(d) Equal path lengths are traversed in equal intervals. 
Ans: If the instantaneous speed v? is positive and constant in a two dimensional 
motion, then due to the scalar nature of speed equal path lengths are traversed in 
equal intervals. 
Hence, the correct answer is (d). 
 
4.8. In a two-dimensional motion, instantaneous speed 
0
v is positive and 
constant. Then which of the following are necessarily true? 
(a) The acceleration of a particle is zero. 
(b) The acceleration of the particle is bounded. 
(c) The acceleration of the particle is necessarily in the plane of motion. 
(d) The particle must be undergoing a uniform circular motion. 
Ans: The acceleration of the particle will necessarily be zero and in the plane of 
motion because the given speed is constant and positive, i.e. in the direction of 
force. 
Hence, the correct answer is (c). 
 
4.9. Three vectors A , B and C add up to zero. Find which is false. 
(a) 
( )
A B C ?? is not zero unless  and BC are parallel. 
(b) 
( )
A B C ?? is not zero unless  and BC are parallel. 
(c) If A , B and C define a place, 
( )
A B C ?? is in that plane. 
(d) 
( )
2 2 2
A B C A B C C A B ? ? ? ? = = + 
Ans: Given that, 0 A B C + + =