DPP – 17-18 TOPIC –UNITS & DIMENSIONS CLASS -
XITH
DPP – 17
Paragraph Q. No. 1 to 3
A particle of mass m moves on the x-axis in a potential energy of the form V(x) = kx2, where k has unit of force
per unit length, it performs simple harmonic motion. X is position on x-axis. The corresponding time period is
proportional to as can be seen easily using dimensional analysis. However, the motion of a particle can be
periodic even when its potential energy increases on both sides of x = 0 in a way different form kx2 and its total
energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the x- axis.
its potential energy is V(x) = αx4 (α > 0) for |x| near the origin and becomes a constant equal to V0 for
Q.1 The acceleration of this particle for can be expressed by
(A*) (B) (C) (D)
Q.2 For periodic motion of small amplitude A, the time period T of this particle is proportional to
(A) (B*) (C) (D)
Q.3 A new physical quantity expressed as . The dimensional formula for quantity
Q & β are respectively:
(B) (C*) (D)
(A)
Q.4 In an experiment of simple pendulum, a student made several observations for the time period of oscillation.
His readings turned out to be 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s. Find (i) mean period of oscillation, (ii)
absolute error in each reading, (iii) mean absolute error, (iv) fractional error and (v) percentage error.
Ans. (i) 2.62s, (ii) -0.01s, 0.06s, 0.02s, -0.09s, -0.18s, (iii) 0.11s (iv) 0.04s, (v) 4%
Q.5 The external and internal diameters of a hollow cylinder measured by a vernier calliper are recorded as (5.32 ±
0.01) cm and (4.98 ± 0.01) cm. compute the thickness of the wall of the cylinder with error limits.
Ans.
Q.6 The measured length and breadth of a rectangle are written as (5.7 ± 0.1) cm and (3.4 ± 0.2) cm respectively.
Calculate the area of the rectangle with error limits.
Ans.
Q.7 The length and breadth of a rectangular sheet are measured to be 5.7 cm and 3.4 cm respectively by an
ordinary scale reading up to 0.1 cm. Find the percentage error in the area of the sheet.
Ans. 4.7%
Q.8 The potential difference across the ends of a wire has been measured to be (100 ± 5) volt and the current in the
wire as (10 ± 0.2) amp. What is the percentage error in the computed resistance of the wire?
Ans. 7%
Aadhar Edu Solutions : BB-54, Jai Ambey Nagar, Near Tonk Road, Gopalpura 1
Bypass, Jaipur * Mob. 09829169534
XITH
DPP – 17
Paragraph Q. No. 1 to 3
A particle of mass m moves on the x-axis in a potential energy of the form V(x) = kx2, where k has unit of force
per unit length, it performs simple harmonic motion. X is position on x-axis. The corresponding time period is
proportional to as can be seen easily using dimensional analysis. However, the motion of a particle can be
periodic even when its potential energy increases on both sides of x = 0 in a way different form kx2 and its total
energy is such that the particle does not escape to infinity. Consider a particle of mass m moving on the x- axis.
its potential energy is V(x) = αx4 (α > 0) for |x| near the origin and becomes a constant equal to V0 for
Q.1 The acceleration of this particle for can be expressed by
(A*) (B) (C) (D)
Q.2 For periodic motion of small amplitude A, the time period T of this particle is proportional to
(A) (B*) (C) (D)
Q.3 A new physical quantity expressed as . The dimensional formula for quantity
Q & β are respectively:
(B) (C*) (D)
(A)
Q.4 In an experiment of simple pendulum, a student made several observations for the time period of oscillation.
His readings turned out to be 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s. Find (i) mean period of oscillation, (ii)
absolute error in each reading, (iii) mean absolute error, (iv) fractional error and (v) percentage error.
Ans. (i) 2.62s, (ii) -0.01s, 0.06s, 0.02s, -0.09s, -0.18s, (iii) 0.11s (iv) 0.04s, (v) 4%
Q.5 The external and internal diameters of a hollow cylinder measured by a vernier calliper are recorded as (5.32 ±
0.01) cm and (4.98 ± 0.01) cm. compute the thickness of the wall of the cylinder with error limits.
Ans.
Q.6 The measured length and breadth of a rectangle are written as (5.7 ± 0.1) cm and (3.4 ± 0.2) cm respectively.
Calculate the area of the rectangle with error limits.
Ans.
Q.7 The length and breadth of a rectangular sheet are measured to be 5.7 cm and 3.4 cm respectively by an
ordinary scale reading up to 0.1 cm. Find the percentage error in the area of the sheet.
Ans. 4.7%
Q.8 The potential difference across the ends of a wire has been measured to be (100 ± 5) volt and the current in the
wire as (10 ± 0.2) amp. What is the percentage error in the computed resistance of the wire?
Ans. 7%
Aadhar Edu Solutions : BB-54, Jai Ambey Nagar, Near Tonk Road, Gopalpura 1
Bypass, Jaipur * Mob. 09829169534
