Q51. The percentage errors in the measurement of mass and momentum of an object are $1\%$ and $2\%$ respectively. The percentage error in the measurement of kinetic energy of the object will be:
Explanation:
Hint:
Step: Find the percentage error in the measurement of the kinetic energy of the object.
The kinetic energy of the particle is given by;
Therefore, the percentage error in the measurement of the kinetic energy of the object is
Hence, option (4) is the correct answer.
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Exam: NEET – 2024
Q52. A force defined by; $F = \alpha t^2 + \beta t$ acts on a particle at a given time $t.$ The factor which is dimensionless, if $\alpha$ and $\beta$ are constants, is:
- $\alpha t / \beta$
- $\alpha \beta t$
- $\alpha \beta / t$
- $\beta t / \alpha$
Explanation:
Hint: Recall the principle of homogeneity of dimensions.
Step: Find the dimensionless quantity.
According to the principle of homogeneity of dimensions, the dimensions of LHS = dimensions of RHS i.e.,
Therefore, the dimensionless quantity is .
Hence, option (1) is the correct answer.
#454992
Exam: NEET – 2024
Q53. In a vernier callipers, $(N+1)$ divisions of the vernier scale coincide with $N$ divisions of the main scale. If $1$ $\text{MSD}$ represents $0.1~\text{mm}$ , the vernier constant (in $\text{cm}$ ) is:
- $\dfrac{1}{100(N+1)}$
- $100N$
- $10(N+1)$
- $\dfrac{1}{10 N}$
Explanation:
Hint:
Step: Find the vernier constant () in cm.
It is given in the question that
The vernier constant or Least count is given by;
Hence, option (1) is the correct answer.
#454980
Exam: NEET – 2024
Q54. The quantities which have the same dimensions as those of solid angle are:
- stress and angle
- strain and arc
- angular speed and stress
- strain and angle
Explanation:
Hint: Recall the dimensions of the given quantities.
Step: Find the quantities which have the same dimensions as those of solid angles.
The expression of the solid angle is given by;
Therefore, the solid angle is a dimensionless quantity.
The dimensions of strain are given by;
The dimensions of the angle are given by;
Therefore, strain and angle are both dimensionless quantities.
Hence, option (4) is the correct answer.
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Exam: NEET – 2024
Q55. Silly Mistake
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