362458
Assertion : A body, whatever its motion is always at rest in a frame of reference which is fixed to the body itself. Reason : The relative velocity of a body with respect to itself is zero.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
In the frame of reference fixed to the body itself, the body is always at rest because it is not changing its position relative to that frame of reference. By definition, the relative velocity of an object with respect to itself is zero. This means that in its own frame of reference, the body is at rest. The reason provides a correct explanation for why the assertion is true. So correct option is (1).
PHXI03:MOTION IN A STRAIGHT LINE
362459
Two cars \(A\) and \(B\) are moving as shown in figure. Find their time of meeting.
1 \(7s\)
2 \(2s\)
3 \(4s\)
4 \(5s\)
Explanation:
Method – 1 When the two cars meet each other \(\left| {{S_A}} \right| + \left| {{S_B}} \right| = 75\) \(10 \, t + 5 \, t = 75\) \(t = 5 \, \sec\). Method-2 (Relative frame method) We can solve with respect to any car, we do it with respect to car \(B\) \({\overline v _{_{AB}}} = {\overline v _{_A}} - {\overline v _{_B}} = 10\hat i - \left( { - 5\hat i} \right) = 15\hat i\) Here car \(B\) is at rest and car \(A\) is moving with \(15 \, m/s\) w.r.t. \(B\) We can transfer the picture into relative frame as shown in the figure \({s_r} = {u_r}t + \frac{1}{2}{a_r}{t^2}({a_r} = 0)\) \(75 = 15t \Rightarrow t = 5\sec .\)
PHXI03:MOTION IN A STRAIGHT LINE
362460
An elevator, whose floor to ceiling distance is equal to 2.7 \(m\), starts ascending with constant acceleration of \(1.2\,m{s^{ - 2}}.\) 2 sec after the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is
1 \(\sqrt {0.54} s\)
2 \(1s\)
3 \(0.7s\)
4 \(\sqrt 6 s\)
Explanation:
\({S_r} = \frac{1}{2}{a_r}{t^2} \Rightarrow t = \sqrt {\frac{{2.7 \times 2}}{{11}}} = 0.7s\) \({S_r} = \) relative displacement of the bolt w.r.to the elevator \({a_r} = \) relative acceleration of bolt w.r.t. the elevator.
PHXI03:MOTION IN A STRAIGHT LINE
362461
Assertion : If two particles, moving with constant velocities are to meet, the relative velocity must be along the line joining the two particles. Reason : Relative velocity means motion of one particle as viewed from the other.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
For two particles to meet, their relative velocities must be directed along the line joining the two particles. This ensures that they are moving towards each other. Relative velocity refers to the motion of one particle as observed from the frame of reference of the other particle. It takes into account both the magnitude and direction of motion. The reason provides a correct explanation for why the assertion is true. So correct option is (1)
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PHXI03:MOTION IN A STRAIGHT LINE
362458
Assertion : A body, whatever its motion is always at rest in a frame of reference which is fixed to the body itself. Reason : The relative velocity of a body with respect to itself is zero.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
In the frame of reference fixed to the body itself, the body is always at rest because it is not changing its position relative to that frame of reference. By definition, the relative velocity of an object with respect to itself is zero. This means that in its own frame of reference, the body is at rest. The reason provides a correct explanation for why the assertion is true. So correct option is (1).
PHXI03:MOTION IN A STRAIGHT LINE
362459
Two cars \(A\) and \(B\) are moving as shown in figure. Find their time of meeting.
1 \(7s\)
2 \(2s\)
3 \(4s\)
4 \(5s\)
Explanation:
Method – 1 When the two cars meet each other \(\left| {{S_A}} \right| + \left| {{S_B}} \right| = 75\) \(10 \, t + 5 \, t = 75\) \(t = 5 \, \sec\). Method-2 (Relative frame method) We can solve with respect to any car, we do it with respect to car \(B\) \({\overline v _{_{AB}}} = {\overline v _{_A}} - {\overline v _{_B}} = 10\hat i - \left( { - 5\hat i} \right) = 15\hat i\) Here car \(B\) is at rest and car \(A\) is moving with \(15 \, m/s\) w.r.t. \(B\) We can transfer the picture into relative frame as shown in the figure \({s_r} = {u_r}t + \frac{1}{2}{a_r}{t^2}({a_r} = 0)\) \(75 = 15t \Rightarrow t = 5\sec .\)
PHXI03:MOTION IN A STRAIGHT LINE
362460
An elevator, whose floor to ceiling distance is equal to 2.7 \(m\), starts ascending with constant acceleration of \(1.2\,m{s^{ - 2}}.\) 2 sec after the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is
1 \(\sqrt {0.54} s\)
2 \(1s\)
3 \(0.7s\)
4 \(\sqrt 6 s\)
Explanation:
\({S_r} = \frac{1}{2}{a_r}{t^2} \Rightarrow t = \sqrt {\frac{{2.7 \times 2}}{{11}}} = 0.7s\) \({S_r} = \) relative displacement of the bolt w.r.to the elevator \({a_r} = \) relative acceleration of bolt w.r.t. the elevator.
PHXI03:MOTION IN A STRAIGHT LINE
362461
Assertion : If two particles, moving with constant velocities are to meet, the relative velocity must be along the line joining the two particles. Reason : Relative velocity means motion of one particle as viewed from the other.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
For two particles to meet, their relative velocities must be directed along the line joining the two particles. This ensures that they are moving towards each other. Relative velocity refers to the motion of one particle as observed from the frame of reference of the other particle. It takes into account both the magnitude and direction of motion. The reason provides a correct explanation for why the assertion is true. So correct option is (1)
362458
Assertion : A body, whatever its motion is always at rest in a frame of reference which is fixed to the body itself. Reason : The relative velocity of a body with respect to itself is zero.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
In the frame of reference fixed to the body itself, the body is always at rest because it is not changing its position relative to that frame of reference. By definition, the relative velocity of an object with respect to itself is zero. This means that in its own frame of reference, the body is at rest. The reason provides a correct explanation for why the assertion is true. So correct option is (1).
PHXI03:MOTION IN A STRAIGHT LINE
362459
Two cars \(A\) and \(B\) are moving as shown in figure. Find their time of meeting.
1 \(7s\)
2 \(2s\)
3 \(4s\)
4 \(5s\)
Explanation:
Method – 1 When the two cars meet each other \(\left| {{S_A}} \right| + \left| {{S_B}} \right| = 75\) \(10 \, t + 5 \, t = 75\) \(t = 5 \, \sec\). Method-2 (Relative frame method) We can solve with respect to any car, we do it with respect to car \(B\) \({\overline v _{_{AB}}} = {\overline v _{_A}} - {\overline v _{_B}} = 10\hat i - \left( { - 5\hat i} \right) = 15\hat i\) Here car \(B\) is at rest and car \(A\) is moving with \(15 \, m/s\) w.r.t. \(B\) We can transfer the picture into relative frame as shown in the figure \({s_r} = {u_r}t + \frac{1}{2}{a_r}{t^2}({a_r} = 0)\) \(75 = 15t \Rightarrow t = 5\sec .\)
PHXI03:MOTION IN A STRAIGHT LINE
362460
An elevator, whose floor to ceiling distance is equal to 2.7 \(m\), starts ascending with constant acceleration of \(1.2\,m{s^{ - 2}}.\) 2 sec after the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is
1 \(\sqrt {0.54} s\)
2 \(1s\)
3 \(0.7s\)
4 \(\sqrt 6 s\)
Explanation:
\({S_r} = \frac{1}{2}{a_r}{t^2} \Rightarrow t = \sqrt {\frac{{2.7 \times 2}}{{11}}} = 0.7s\) \({S_r} = \) relative displacement of the bolt w.r.to the elevator \({a_r} = \) relative acceleration of bolt w.r.t. the elevator.
PHXI03:MOTION IN A STRAIGHT LINE
362461
Assertion : If two particles, moving with constant velocities are to meet, the relative velocity must be along the line joining the two particles. Reason : Relative velocity means motion of one particle as viewed from the other.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
For two particles to meet, their relative velocities must be directed along the line joining the two particles. This ensures that they are moving towards each other. Relative velocity refers to the motion of one particle as observed from the frame of reference of the other particle. It takes into account both the magnitude and direction of motion. The reason provides a correct explanation for why the assertion is true. So correct option is (1)
362458
Assertion : A body, whatever its motion is always at rest in a frame of reference which is fixed to the body itself. Reason : The relative velocity of a body with respect to itself is zero.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
In the frame of reference fixed to the body itself, the body is always at rest because it is not changing its position relative to that frame of reference. By definition, the relative velocity of an object with respect to itself is zero. This means that in its own frame of reference, the body is at rest. The reason provides a correct explanation for why the assertion is true. So correct option is (1).
PHXI03:MOTION IN A STRAIGHT LINE
362459
Two cars \(A\) and \(B\) are moving as shown in figure. Find their time of meeting.
1 \(7s\)
2 \(2s\)
3 \(4s\)
4 \(5s\)
Explanation:
Method – 1 When the two cars meet each other \(\left| {{S_A}} \right| + \left| {{S_B}} \right| = 75\) \(10 \, t + 5 \, t = 75\) \(t = 5 \, \sec\). Method-2 (Relative frame method) We can solve with respect to any car, we do it with respect to car \(B\) \({\overline v _{_{AB}}} = {\overline v _{_A}} - {\overline v _{_B}} = 10\hat i - \left( { - 5\hat i} \right) = 15\hat i\) Here car \(B\) is at rest and car \(A\) is moving with \(15 \, m/s\) w.r.t. \(B\) We can transfer the picture into relative frame as shown in the figure \({s_r} = {u_r}t + \frac{1}{2}{a_r}{t^2}({a_r} = 0)\) \(75 = 15t \Rightarrow t = 5\sec .\)
PHXI03:MOTION IN A STRAIGHT LINE
362460
An elevator, whose floor to ceiling distance is equal to 2.7 \(m\), starts ascending with constant acceleration of \(1.2\,m{s^{ - 2}}.\) 2 sec after the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is
1 \(\sqrt {0.54} s\)
2 \(1s\)
3 \(0.7s\)
4 \(\sqrt 6 s\)
Explanation:
\({S_r} = \frac{1}{2}{a_r}{t^2} \Rightarrow t = \sqrt {\frac{{2.7 \times 2}}{{11}}} = 0.7s\) \({S_r} = \) relative displacement of the bolt w.r.to the elevator \({a_r} = \) relative acceleration of bolt w.r.t. the elevator.
PHXI03:MOTION IN A STRAIGHT LINE
362461
Assertion : If two particles, moving with constant velocities are to meet, the relative velocity must be along the line joining the two particles. Reason : Relative velocity means motion of one particle as viewed from the other.
1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
For two particles to meet, their relative velocities must be directed along the line joining the two particles. This ensures that they are moving towards each other. Relative velocity refers to the motion of one particle as observed from the frame of reference of the other particle. It takes into account both the magnitude and direction of motion. The reason provides a correct explanation for why the assertion is true. So correct option is (1)
