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The quantities which have the same dimensions as those of solid angle are:
The figure shows the elliptical orbit of a planet $m$ about the sun $S$. The shaded area $SCD$ is twice the shaded area $SAB$. If $t_1$ is the time for the planet to move from $C$ to $D$ and $t_2$ is the time to move from $A$ to $B$, then:
The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively $4\%$ and $2\%$. The maximum error in the measurement of pressure is
Increase in temperature of a gas filled in a container would lead to :
A body of mass $m$ is taken from the Earth’s surface to the height equal to twice the radius ($R$) of the Earth. The change in potential energy of the body will be:
The earth is assumed to be a sphere of radius $R$. A platform is arranged at a height $R$ from the surface of the earth. The escape velocity of a body from this platform is $fv_e$, where $v_e$ is its escape velocity from the surface of the earth. The value of $f$ is:
Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful?
A vernier calipers has 1 mm marks on the main scale. It has 20 equal divisions on the vernier scale which match with 16 main scale divisions. The least count of this vernier calipers is:
An infinite number of bodies, each of mass $2 \text{ kg}$ are situated on the $x$-axis at distances $1 \text{ m}, 2 \text{ m}, 4 \text{ m}, 8 \text{ m}, ......$ respectively, from the origin. The resulting gravitational potential due to this system at the origin will be:
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 cm) is:
A body weighs $200 \text{ N}$ on the surface of the earth. How much will it weigh halfway down the centre of the earth?
The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are:
A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate $g$, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are $e_1$ and $e_2$ respectively, the percentage error in the estimation of $g$ is
If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is:
A thin flat circular disc of radius $4.5 \text{ cm}$ is placed gently over the surface of water. If the surface tension of water is $0.07 \text{ N m}^{-1}$, then the excess force required to take it away from the surface is:
The diameter of a spherical bob, when measured with vernier callipers yielded the values: 3.33 cm, 3.32 cm, 3.34 cm, 3.33 cm and 3.32 cm. The mean diameter to appropriate significant figures is:
The physical quantity that has the same dimensional formula as pressure is:
A small hole of an area of cross-section $2 \text{ mm}^2$ is present near the bottom of a fully filled open tank of height $2 \text{ m}$. Taking $g = 10 \text{ m/s}^2$, the rate of flow of water through the open hole would be nearly:
The approximate depth of an ocean is $2700 \text{ m}$. The compressibility of water is $45.4 \times 10^{-11} \text{ Pa}^{-1}$ and the density of water is $10^3 \text{ kg/m}^3$. What fractional compression of water will be obtained at the bottom of the ocean?
Match List- I with List- II. List-I (Measured values) (A) 0.001213 (B) $2.1 \times 10^{16}$ (C) 3.70 (D) 3000 List-II (Significant figures) (I) 2 (II) 3 (III) 1 (IV) 4